2000 character limit reached
Quantum Quench Dynamics of Geometrically Frustrated Ising Models
Published 29 Feb 2024 in quant-ph | (2403.00091v1)
Abstract: Geometric frustration in two-dimensional Ising models allows for a wealth of exotic universal behavior, both Ising and non-Ising, in the presence of quantum fluctuations. In particular, the triangular antiferromagnet and Villain model in a transverse field can be understood through distinct XY pseudospins, but have qualitatively similar phase diagrams including a quantum phase transition in the (2+1)-dimensional XY universality class. While the quantum dynamics of modestly-sized systems can be simulated classically using tensor-based methods, these methods become infeasible for larger lattices. Here we perform both classical and quantum simulations of these dynamics, where our quantum simulator is a superconducting quantum annealer. Our observations on the triangular lattice suggest that the dominant quench dynamics are not described by the quantum Kibble-Zurek scaling of the quantum phase transition, but rather a faster coarsening dynamics in an effective two-dimensional XY model in the ordered phase. Similarly, on the Villain model, the scaling exponent does not match the Kibble-Zurek expectation. These results demonstrate the ability of quantum annealers to simulate coherent quantum dynamics and scale beyond the reach of classical approaches.
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URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Shaginyan, V. R. et al. Theoretical and experimental developments in quantum spin liquid in geometrically frustrated magnets: A review - journal of materials science (2019). URL https://link.springer.com/article/10.1007/s10853-019-04128-w. [3] Moessner, R. & Sondhi, S. L. Ising models of quantum frustration. Physical Review B 63, 1–19 (2001). [4] Anderson, P. W. Resonating valence bonds: A new kind of insulator? Materials Research Bulletin 8, 153–160 (1973). [5] Savary, L. & Balents, L. Quantum spin liquids: a review. Reports on Progress in Physics 80, 016502 (2016). URL https://dx.doi.org/10.1088/0034-4885/80/1/016502. [6] Teo, J. C. & Hughes, T. L. Topological defects in symmetry-protected topological phases. Annual Review of Condensed Matter Physics 8, 211–237 (2017). URL https://doi.org/10.1146/annurev-conmatphys-031016-025154. [7] Blankschtein, D., Ma, M., Berker, A. N., Grest, G. S. & Soukoulis, C. M. Orderings of a stacked frustrated triangular system in three dimensions. Physical Review B 29, 5250–5252 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.29.5250. [8] Blankschtein, D., Ma, M. & Berker, A. N. Fully and partially frustrated simple-cubic Ising models: Landau-Ginzburg-Wilson theory. Physical Review B 30, 1362–1365 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.30.1362. [9] Sachdev, S. Quantum phase transitions. Physics world 12, 33 (1999). [10] Jalabert, R. A. & Sachdev, S. Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model. Physical Review B 44, 686–690 (1991). URL https://link.aps.org/doi/10.1103/PhysRevB.44.686. [11] Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Moessner, R. & Sondhi, S. L. Ising models of quantum frustration. Physical Review B 63, 1–19 (2001). [4] Anderson, P. W. Resonating valence bonds: A new kind of insulator? Materials Research Bulletin 8, 153–160 (1973). [5] Savary, L. & Balents, L. Quantum spin liquids: a review. Reports on Progress in Physics 80, 016502 (2016). URL https://dx.doi.org/10.1088/0034-4885/80/1/016502. [6] Teo, J. C. & Hughes, T. L. Topological defects in symmetry-protected topological phases. Annual Review of Condensed Matter Physics 8, 211–237 (2017). URL https://doi.org/10.1146/annurev-conmatphys-031016-025154. [7] Blankschtein, D., Ma, M., Berker, A. N., Grest, G. S. & Soukoulis, C. M. Orderings of a stacked frustrated triangular system in three dimensions. Physical Review B 29, 5250–5252 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.29.5250. [8] Blankschtein, D., Ma, M. & Berker, A. N. Fully and partially frustrated simple-cubic Ising models: Landau-Ginzburg-Wilson theory. Physical Review B 30, 1362–1365 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.30.1362. [9] Sachdev, S. Quantum phase transitions. Physics world 12, 33 (1999). [10] Jalabert, R. A. & Sachdev, S. Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model. Physical Review B 44, 686–690 (1991). URL https://link.aps.org/doi/10.1103/PhysRevB.44.686. [11] Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Anderson, P. W. Resonating valence bonds: A new kind of insulator? Materials Research Bulletin 8, 153–160 (1973). [5] Savary, L. & Balents, L. Quantum spin liquids: a review. Reports on Progress in Physics 80, 016502 (2016). URL https://dx.doi.org/10.1088/0034-4885/80/1/016502. [6] Teo, J. C. & Hughes, T. L. Topological defects in symmetry-protected topological phases. Annual Review of Condensed Matter Physics 8, 211–237 (2017). URL https://doi.org/10.1146/annurev-conmatphys-031016-025154. [7] Blankschtein, D., Ma, M., Berker, A. N., Grest, G. S. & Soukoulis, C. M. Orderings of a stacked frustrated triangular system in three dimensions. Physical Review B 29, 5250–5252 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.29.5250. [8] Blankschtein, D., Ma, M. & Berker, A. N. Fully and partially frustrated simple-cubic Ising models: Landau-Ginzburg-Wilson theory. Physical Review B 30, 1362–1365 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.30.1362. [9] Sachdev, S. Quantum phase transitions. Physics world 12, 33 (1999). [10] Jalabert, R. A. & Sachdev, S. Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model. Physical Review B 44, 686–690 (1991). URL https://link.aps.org/doi/10.1103/PhysRevB.44.686. [11] Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Savary, L. & Balents, L. Quantum spin liquids: a review. Reports on Progress in Physics 80, 016502 (2016). URL https://dx.doi.org/10.1088/0034-4885/80/1/016502. [6] Teo, J. C. & Hughes, T. L. Topological defects in symmetry-protected topological phases. Annual Review of Condensed Matter Physics 8, 211–237 (2017). URL https://doi.org/10.1146/annurev-conmatphys-031016-025154. [7] Blankschtein, D., Ma, M., Berker, A. N., Grest, G. S. & Soukoulis, C. M. Orderings of a stacked frustrated triangular system in three dimensions. Physical Review B 29, 5250–5252 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.29.5250. [8] Blankschtein, D., Ma, M. & Berker, A. N. Fully and partially frustrated simple-cubic Ising models: Landau-Ginzburg-Wilson theory. Physical Review B 30, 1362–1365 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.30.1362. [9] Sachdev, S. Quantum phase transitions. Physics world 12, 33 (1999). [10] Jalabert, R. A. & Sachdev, S. Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model. Physical Review B 44, 686–690 (1991). URL https://link.aps.org/doi/10.1103/PhysRevB.44.686. [11] Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Teo, J. C. & Hughes, T. L. Topological defects in symmetry-protected topological phases. Annual Review of Condensed Matter Physics 8, 211–237 (2017). URL https://doi.org/10.1146/annurev-conmatphys-031016-025154. [7] Blankschtein, D., Ma, M., Berker, A. N., Grest, G. S. & Soukoulis, C. M. Orderings of a stacked frustrated triangular system in three dimensions. Physical Review B 29, 5250–5252 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.29.5250. [8] Blankschtein, D., Ma, M. & Berker, A. N. Fully and partially frustrated simple-cubic Ising models: Landau-Ginzburg-Wilson theory. Physical Review B 30, 1362–1365 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.30.1362. [9] Sachdev, S. Quantum phase transitions. Physics world 12, 33 (1999). [10] Jalabert, R. A. & Sachdev, S. Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model. Physical Review B 44, 686–690 (1991). URL https://link.aps.org/doi/10.1103/PhysRevB.44.686. [11] Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Blankschtein, D., Ma, M., Berker, A. N., Grest, G. S. & Soukoulis, C. M. Orderings of a stacked frustrated triangular system in three dimensions. Physical Review B 29, 5250–5252 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.29.5250. [8] Blankschtein, D., Ma, M. & Berker, A. N. Fully and partially frustrated simple-cubic Ising models: Landau-Ginzburg-Wilson theory. Physical Review B 30, 1362–1365 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.30.1362. [9] Sachdev, S. Quantum phase transitions. Physics world 12, 33 (1999). [10] Jalabert, R. A. & Sachdev, S. Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model. Physical Review B 44, 686–690 (1991). URL https://link.aps.org/doi/10.1103/PhysRevB.44.686. [11] Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Blankschtein, D., Ma, M. & Berker, A. N. Fully and partially frustrated simple-cubic Ising models: Landau-Ginzburg-Wilson theory. Physical Review B 30, 1362–1365 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.30.1362. [9] Sachdev, S. Quantum phase transitions. Physics world 12, 33 (1999). [10] Jalabert, R. A. & Sachdev, S. Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model. Physical Review B 44, 686–690 (1991). URL https://link.aps.org/doi/10.1103/PhysRevB.44.686. [11] Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Sachdev, S. Quantum phase transitions. Physics world 12, 33 (1999). [10] Jalabert, R. A. & Sachdev, S. Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model. Physical Review B 44, 686–690 (1991). URL https://link.aps.org/doi/10.1103/PhysRevB.44.686. [11] Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Jalabert, R. A. & Sachdev, S. Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model. Physical Review B 44, 686–690 (1991). URL https://link.aps.org/doi/10.1103/PhysRevB.44.686. [11] Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014).
- Shaginyan, V. R. et al. Theoretical and experimental developments in quantum spin liquid in geometrically frustrated magnets: A review - journal of materials science (2019). URL https://link.springer.com/article/10.1007/s10853-019-04128-w. [3] Moessner, R. & Sondhi, S. L. Ising models of quantum frustration. Physical Review B 63, 1–19 (2001). [4] Anderson, P. W. Resonating valence bonds: A new kind of insulator? Materials Research Bulletin 8, 153–160 (1973). [5] Savary, L. & Balents, L. Quantum spin liquids: a review. Reports on Progress in Physics 80, 016502 (2016). URL https://dx.doi.org/10.1088/0034-4885/80/1/016502. [6] Teo, J. C. & Hughes, T. L. Topological defects in symmetry-protected topological phases. Annual Review of Condensed Matter Physics 8, 211–237 (2017). URL https://doi.org/10.1146/annurev-conmatphys-031016-025154. [7] Blankschtein, D., Ma, M., Berker, A. N., Grest, G. S. & Soukoulis, C. M. Orderings of a stacked frustrated triangular system in three dimensions. Physical Review B 29, 5250–5252 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.29.5250. [8] Blankschtein, D., Ma, M. & Berker, A. N. Fully and partially frustrated simple-cubic Ising models: Landau-Ginzburg-Wilson theory. Physical Review B 30, 1362–1365 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.30.1362. [9] Sachdev, S. Quantum phase transitions. Physics world 12, 33 (1999). [10] Jalabert, R. A. & Sachdev, S. Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model. Physical Review B 44, 686–690 (1991). URL https://link.aps.org/doi/10.1103/PhysRevB.44.686. [11] Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Moessner, R. & Sondhi, S. L. Ising models of quantum frustration. Physical Review B 63, 1–19 (2001). [4] Anderson, P. W. Resonating valence bonds: A new kind of insulator? Materials Research Bulletin 8, 153–160 (1973). [5] Savary, L. & Balents, L. Quantum spin liquids: a review. Reports on Progress in Physics 80, 016502 (2016). URL https://dx.doi.org/10.1088/0034-4885/80/1/016502. [6] Teo, J. C. & Hughes, T. L. Topological defects in symmetry-protected topological phases. Annual Review of Condensed Matter Physics 8, 211–237 (2017). URL https://doi.org/10.1146/annurev-conmatphys-031016-025154. [7] Blankschtein, D., Ma, M., Berker, A. N., Grest, G. S. & Soukoulis, C. M. Orderings of a stacked frustrated triangular system in three dimensions. Physical Review B 29, 5250–5252 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.29.5250. [8] Blankschtein, D., Ma, M. & Berker, A. N. Fully and partially frustrated simple-cubic Ising models: Landau-Ginzburg-Wilson theory. Physical Review B 30, 1362–1365 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.30.1362. [9] Sachdev, S. Quantum phase transitions. Physics world 12, 33 (1999). [10] Jalabert, R. A. & Sachdev, S. Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model. Physical Review B 44, 686–690 (1991). URL https://link.aps.org/doi/10.1103/PhysRevB.44.686. [11] Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Anderson, P. W. Resonating valence bonds: A new kind of insulator? Materials Research Bulletin 8, 153–160 (1973). [5] Savary, L. & Balents, L. Quantum spin liquids: a review. Reports on Progress in Physics 80, 016502 (2016). URL https://dx.doi.org/10.1088/0034-4885/80/1/016502. [6] Teo, J. C. & Hughes, T. L. Topological defects in symmetry-protected topological phases. Annual Review of Condensed Matter Physics 8, 211–237 (2017). URL https://doi.org/10.1146/annurev-conmatphys-031016-025154. [7] Blankschtein, D., Ma, M., Berker, A. N., Grest, G. S. & Soukoulis, C. M. Orderings of a stacked frustrated triangular system in three dimensions. Physical Review B 29, 5250–5252 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.29.5250. [8] Blankschtein, D., Ma, M. & Berker, A. N. Fully and partially frustrated simple-cubic Ising models: Landau-Ginzburg-Wilson theory. Physical Review B 30, 1362–1365 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.30.1362. [9] Sachdev, S. Quantum phase transitions. Physics world 12, 33 (1999). [10] Jalabert, R. A. & Sachdev, S. Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model. Physical Review B 44, 686–690 (1991). URL https://link.aps.org/doi/10.1103/PhysRevB.44.686. [11] Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Savary, L. & Balents, L. Quantum spin liquids: a review. Reports on Progress in Physics 80, 016502 (2016). URL https://dx.doi.org/10.1088/0034-4885/80/1/016502. [6] Teo, J. C. & Hughes, T. L. Topological defects in symmetry-protected topological phases. Annual Review of Condensed Matter Physics 8, 211–237 (2017). URL https://doi.org/10.1146/annurev-conmatphys-031016-025154. [7] Blankschtein, D., Ma, M., Berker, A. N., Grest, G. S. & Soukoulis, C. M. Orderings of a stacked frustrated triangular system in three dimensions. Physical Review B 29, 5250–5252 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.29.5250. [8] Blankschtein, D., Ma, M. & Berker, A. N. Fully and partially frustrated simple-cubic Ising models: Landau-Ginzburg-Wilson theory. Physical Review B 30, 1362–1365 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.30.1362. [9] Sachdev, S. Quantum phase transitions. Physics world 12, 33 (1999). [10] Jalabert, R. A. & Sachdev, S. Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model. Physical Review B 44, 686–690 (1991). URL https://link.aps.org/doi/10.1103/PhysRevB.44.686. [11] Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Teo, J. C. & Hughes, T. L. Topological defects in symmetry-protected topological phases. Annual Review of Condensed Matter Physics 8, 211–237 (2017). URL https://doi.org/10.1146/annurev-conmatphys-031016-025154. [7] Blankschtein, D., Ma, M., Berker, A. N., Grest, G. S. & Soukoulis, C. M. Orderings of a stacked frustrated triangular system in three dimensions. Physical Review B 29, 5250–5252 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.29.5250. [8] Blankschtein, D., Ma, M. & Berker, A. N. Fully and partially frustrated simple-cubic Ising models: Landau-Ginzburg-Wilson theory. Physical Review B 30, 1362–1365 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.30.1362. [9] Sachdev, S. Quantum phase transitions. Physics world 12, 33 (1999). [10] Jalabert, R. A. & Sachdev, S. Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model. Physical Review B 44, 686–690 (1991). URL https://link.aps.org/doi/10.1103/PhysRevB.44.686. [11] Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Blankschtein, D., Ma, M., Berker, A. N., Grest, G. S. & Soukoulis, C. M. Orderings of a stacked frustrated triangular system in three dimensions. Physical Review B 29, 5250–5252 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.29.5250. [8] Blankschtein, D., Ma, M. & Berker, A. N. Fully and partially frustrated simple-cubic Ising models: Landau-Ginzburg-Wilson theory. Physical Review B 30, 1362–1365 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.30.1362. [9] Sachdev, S. Quantum phase transitions. Physics world 12, 33 (1999). [10] Jalabert, R. A. & Sachdev, S. Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model. Physical Review B 44, 686–690 (1991). URL https://link.aps.org/doi/10.1103/PhysRevB.44.686. [11] Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Blankschtein, D., Ma, M. & Berker, A. N. Fully and partially frustrated simple-cubic Ising models: Landau-Ginzburg-Wilson theory. Physical Review B 30, 1362–1365 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.30.1362. [9] Sachdev, S. Quantum phase transitions. Physics world 12, 33 (1999). [10] Jalabert, R. A. & Sachdev, S. Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model. Physical Review B 44, 686–690 (1991). URL https://link.aps.org/doi/10.1103/PhysRevB.44.686. [11] Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Sachdev, S. Quantum phase transitions. Physics world 12, 33 (1999). [10] Jalabert, R. A. & Sachdev, S. Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model. Physical Review B 44, 686–690 (1991). URL https://link.aps.org/doi/10.1103/PhysRevB.44.686. [11] Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Jalabert, R. A. & Sachdev, S. Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model. Physical Review B 44, 686–690 (1991). URL https://link.aps.org/doi/10.1103/PhysRevB.44.686. [11] Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. 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[24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014).
- Ising models of quantum frustration. Physical Review B 63, 1–19 (2001). [4] Anderson, P. W. Resonating valence bonds: A new kind of insulator? Materials Research Bulletin 8, 153–160 (1973). [5] Savary, L. & Balents, L. Quantum spin liquids: a review. Reports on Progress in Physics 80, 016502 (2016). URL https://dx.doi.org/10.1088/0034-4885/80/1/016502. [6] Teo, J. C. & Hughes, T. L. Topological defects in symmetry-protected topological phases. Annual Review of Condensed Matter Physics 8, 211–237 (2017). URL https://doi.org/10.1146/annurev-conmatphys-031016-025154. [7] Blankschtein, D., Ma, M., Berker, A. N., Grest, G. S. & Soukoulis, C. M. Orderings of a stacked frustrated triangular system in three dimensions. Physical Review B 29, 5250–5252 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.29.5250. [8] Blankschtein, D., Ma, M. & Berker, A. N. Fully and partially frustrated simple-cubic Ising models: Landau-Ginzburg-Wilson theory. Physical Review B 30, 1362–1365 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.30.1362. [9] Sachdev, S. Quantum phase transitions. Physics world 12, 33 (1999). [10] Jalabert, R. A. & Sachdev, S. Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model. Physical Review B 44, 686–690 (1991). URL https://link.aps.org/doi/10.1103/PhysRevB.44.686. [11] Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Anderson, P. W. Resonating valence bonds: A new kind of insulator? Materials Research Bulletin 8, 153–160 (1973). [5] Savary, L. & Balents, L. Quantum spin liquids: a review. Reports on Progress in Physics 80, 016502 (2016). URL https://dx.doi.org/10.1088/0034-4885/80/1/016502. [6] Teo, J. C. & Hughes, T. L. Topological defects in symmetry-protected topological phases. Annual Review of Condensed Matter Physics 8, 211–237 (2017). URL https://doi.org/10.1146/annurev-conmatphys-031016-025154. [7] Blankschtein, D., Ma, M., Berker, A. N., Grest, G. S. & Soukoulis, C. M. Orderings of a stacked frustrated triangular system in three dimensions. Physical Review B 29, 5250–5252 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.29.5250. [8] Blankschtein, D., Ma, M. & Berker, A. N. Fully and partially frustrated simple-cubic Ising models: Landau-Ginzburg-Wilson theory. Physical Review B 30, 1362–1365 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.30.1362. [9] Sachdev, S. Quantum phase transitions. Physics world 12, 33 (1999). [10] Jalabert, R. A. & Sachdev, S. Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model. Physical Review B 44, 686–690 (1991). URL https://link.aps.org/doi/10.1103/PhysRevB.44.686. [11] Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Savary, L. & Balents, L. Quantum spin liquids: a review. Reports on Progress in Physics 80, 016502 (2016). URL https://dx.doi.org/10.1088/0034-4885/80/1/016502. [6] Teo, J. C. & Hughes, T. L. Topological defects in symmetry-protected topological phases. Annual Review of Condensed Matter Physics 8, 211–237 (2017). URL https://doi.org/10.1146/annurev-conmatphys-031016-025154. [7] Blankschtein, D., Ma, M., Berker, A. N., Grest, G. S. & Soukoulis, C. M. Orderings of a stacked frustrated triangular system in three dimensions. Physical Review B 29, 5250–5252 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.29.5250. [8] Blankschtein, D., Ma, M. & Berker, A. N. Fully and partially frustrated simple-cubic Ising models: Landau-Ginzburg-Wilson theory. Physical Review B 30, 1362–1365 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.30.1362. [9] Sachdev, S. Quantum phase transitions. Physics world 12, 33 (1999). [10] Jalabert, R. A. & Sachdev, S. Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model. Physical Review B 44, 686–690 (1991). URL https://link.aps.org/doi/10.1103/PhysRevB.44.686. [11] Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Teo, J. C. & Hughes, T. L. Topological defects in symmetry-protected topological phases. Annual Review of Condensed Matter Physics 8, 211–237 (2017). URL https://doi.org/10.1146/annurev-conmatphys-031016-025154. [7] Blankschtein, D., Ma, M., Berker, A. N., Grest, G. S. & Soukoulis, C. M. Orderings of a stacked frustrated triangular system in three dimensions. Physical Review B 29, 5250–5252 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.29.5250. [8] Blankschtein, D., Ma, M. & Berker, A. N. Fully and partially frustrated simple-cubic Ising models: Landau-Ginzburg-Wilson theory. Physical Review B 30, 1362–1365 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.30.1362. [9] Sachdev, S. Quantum phase transitions. Physics world 12, 33 (1999). [10] Jalabert, R. A. & Sachdev, S. Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model. Physical Review B 44, 686–690 (1991). URL https://link.aps.org/doi/10.1103/PhysRevB.44.686. [11] Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Blankschtein, D., Ma, M., Berker, A. N., Grest, G. S. & Soukoulis, C. M. Orderings of a stacked frustrated triangular system in three dimensions. Physical Review B 29, 5250–5252 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.29.5250. [8] Blankschtein, D., Ma, M. & Berker, A. N. Fully and partially frustrated simple-cubic Ising models: Landau-Ginzburg-Wilson theory. Physical Review B 30, 1362–1365 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.30.1362. [9] Sachdev, S. Quantum phase transitions. Physics world 12, 33 (1999). [10] Jalabert, R. A. & Sachdev, S. Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model. Physical Review B 44, 686–690 (1991). URL https://link.aps.org/doi/10.1103/PhysRevB.44.686. [11] Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Blankschtein, D., Ma, M. & Berker, A. N. Fully and partially frustrated simple-cubic Ising models: Landau-Ginzburg-Wilson theory. Physical Review B 30, 1362–1365 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.30.1362. [9] Sachdev, S. Quantum phase transitions. Physics world 12, 33 (1999). [10] Jalabert, R. A. & Sachdev, S. Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model. Physical Review B 44, 686–690 (1991). URL https://link.aps.org/doi/10.1103/PhysRevB.44.686. [11] Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Sachdev, S. Quantum phase transitions. Physics world 12, 33 (1999). [10] Jalabert, R. A. & Sachdev, S. Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model. Physical Review B 44, 686–690 (1991). URL https://link.aps.org/doi/10.1103/PhysRevB.44.686. [11] Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Jalabert, R. A. & Sachdev, S. Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model. Physical Review B 44, 686–690 (1991). URL https://link.aps.org/doi/10.1103/PhysRevB.44.686. [11] Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014).
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Quantum phase transitions. Physics world 12, 33 (1999). [10] Jalabert, R. A. & Sachdev, S. Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model. Physical Review B 44, 686–690 (1991). URL https://link.aps.org/doi/10.1103/PhysRevB.44.686. [11] Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Savary, L. & Balents, L. Quantum spin liquids: a review. Reports on Progress in Physics 80, 016502 (2016). URL https://dx.doi.org/10.1088/0034-4885/80/1/016502. [6] Teo, J. C. & Hughes, T. L. Topological defects in symmetry-protected topological phases. Annual Review of Condensed Matter Physics 8, 211–237 (2017). URL https://doi.org/10.1146/annurev-conmatphys-031016-025154. [7] Blankschtein, D., Ma, M., Berker, A. N., Grest, G. S. & Soukoulis, C. M. Orderings of a stacked frustrated triangular system in three dimensions. Physical Review B 29, 5250–5252 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.29.5250. [8] Blankschtein, D., Ma, M. & Berker, A. N. Fully and partially frustrated simple-cubic Ising models: Landau-Ginzburg-Wilson theory. Physical Review B 30, 1362–1365 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.30.1362. [9] Sachdev, S. Quantum phase transitions. Physics world 12, 33 (1999). [10] Jalabert, R. A. & Sachdev, S. Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model. Physical Review B 44, 686–690 (1991). URL https://link.aps.org/doi/10.1103/PhysRevB.44.686. [11] Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Teo, J. C. & Hughes, T. L. Topological defects in symmetry-protected topological phases. Annual Review of Condensed Matter Physics 8, 211–237 (2017). URL https://doi.org/10.1146/annurev-conmatphys-031016-025154. [7] Blankschtein, D., Ma, M., Berker, A. N., Grest, G. S. & Soukoulis, C. M. Orderings of a stacked frustrated triangular system in three dimensions. Physical Review B 29, 5250–5252 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.29.5250. [8] Blankschtein, D., Ma, M. & Berker, A. N. Fully and partially frustrated simple-cubic Ising models: Landau-Ginzburg-Wilson theory. Physical Review B 30, 1362–1365 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.30.1362. [9] Sachdev, S. Quantum phase transitions. Physics world 12, 33 (1999). [10] Jalabert, R. A. & Sachdev, S. Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model. Physical Review B 44, 686–690 (1991). URL https://link.aps.org/doi/10.1103/PhysRevB.44.686. [11] Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Blankschtein, D., Ma, M., Berker, A. N., Grest, G. S. & Soukoulis, C. M. Orderings of a stacked frustrated triangular system in three dimensions. Physical Review B 29, 5250–5252 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.29.5250. [8] Blankschtein, D., Ma, M. & Berker, A. N. Fully and partially frustrated simple-cubic Ising models: Landau-Ginzburg-Wilson theory. Physical Review B 30, 1362–1365 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.30.1362. [9] Sachdev, S. Quantum phase transitions. Physics world 12, 33 (1999). [10] Jalabert, R. A. & Sachdev, S. Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model. Physical Review B 44, 686–690 (1991). URL https://link.aps.org/doi/10.1103/PhysRevB.44.686. [11] Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Blankschtein, D., Ma, M. & Berker, A. N. Fully and partially frustrated simple-cubic Ising models: Landau-Ginzburg-Wilson theory. Physical Review B 30, 1362–1365 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.30.1362. [9] Sachdev, S. Quantum phase transitions. Physics world 12, 33 (1999). [10] Jalabert, R. A. & Sachdev, S. Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model. Physical Review B 44, 686–690 (1991). URL https://link.aps.org/doi/10.1103/PhysRevB.44.686. [11] Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Sachdev, S. Quantum phase transitions. Physics world 12, 33 (1999). [10] Jalabert, R. A. & Sachdev, S. Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model. Physical Review B 44, 686–690 (1991). URL https://link.aps.org/doi/10.1103/PhysRevB.44.686. [11] Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Jalabert, R. A. & Sachdev, S. Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model. Physical Review B 44, 686–690 (1991). URL https://link.aps.org/doi/10.1103/PhysRevB.44.686. [11] Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. 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Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. 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[30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. 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Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. 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Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. 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Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Teo, J. C. & Hughes, T. L. Topological defects in symmetry-protected topological phases. Annual Review of Condensed Matter Physics 8, 211–237 (2017). URL https://doi.org/10.1146/annurev-conmatphys-031016-025154. [7] Blankschtein, D., Ma, M., Berker, A. N., Grest, G. S. & Soukoulis, C. M. Orderings of a stacked frustrated triangular system in three dimensions. Physical Review B 29, 5250–5252 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.29.5250. [8] Blankschtein, D., Ma, M. & Berker, A. N. Fully and partially frustrated simple-cubic Ising models: Landau-Ginzburg-Wilson theory. Physical Review B 30, 1362–1365 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.30.1362. [9] Sachdev, S. Quantum phase transitions. Physics world 12, 33 (1999). [10] Jalabert, R. A. & Sachdev, S. Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model. Physical Review B 44, 686–690 (1991). URL https://link.aps.org/doi/10.1103/PhysRevB.44.686. [11] Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Blankschtein, D., Ma, M., Berker, A. N., Grest, G. S. & Soukoulis, C. M. Orderings of a stacked frustrated triangular system in three dimensions. Physical Review B 29, 5250–5252 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.29.5250. [8] Blankschtein, D., Ma, M. & Berker, A. N. Fully and partially frustrated simple-cubic Ising models: Landau-Ginzburg-Wilson theory. Physical Review B 30, 1362–1365 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.30.1362. [9] Sachdev, S. Quantum phase transitions. Physics world 12, 33 (1999). [10] Jalabert, R. A. & Sachdev, S. Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model. Physical Review B 44, 686–690 (1991). URL https://link.aps.org/doi/10.1103/PhysRevB.44.686. [11] Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Blankschtein, D., Ma, M. & Berker, A. N. Fully and partially frustrated simple-cubic Ising models: Landau-Ginzburg-Wilson theory. Physical Review B 30, 1362–1365 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.30.1362. [9] Sachdev, S. Quantum phase transitions. Physics world 12, 33 (1999). [10] Jalabert, R. A. & Sachdev, S. Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model. Physical Review B 44, 686–690 (1991). URL https://link.aps.org/doi/10.1103/PhysRevB.44.686. [11] Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Sachdev, S. Quantum phase transitions. Physics world 12, 33 (1999). [10] Jalabert, R. A. & Sachdev, S. Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model. Physical Review B 44, 686–690 (1991). URL https://link.aps.org/doi/10.1103/PhysRevB.44.686. [11] Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Jalabert, R. A. & Sachdev, S. Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model. Physical Review B 44, 686–690 (1991). URL https://link.aps.org/doi/10.1103/PhysRevB.44.686. [11] Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. 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Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. 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[30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014).
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[28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Blankschtein, D., Ma, M., Berker, A. N., Grest, G. S. & Soukoulis, C. M. Orderings of a stacked frustrated triangular system in three dimensions. Physical Review B 29, 5250–5252 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.29.5250. [8] Blankschtein, D., Ma, M. & Berker, A. N. Fully and partially frustrated simple-cubic Ising models: Landau-Ginzburg-Wilson theory. Physical Review B 30, 1362–1365 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.30.1362. [9] Sachdev, S. Quantum phase transitions. Physics world 12, 33 (1999). [10] Jalabert, R. A. & Sachdev, S. Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model. Physical Review B 44, 686–690 (1991). URL https://link.aps.org/doi/10.1103/PhysRevB.44.686. [11] Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Blankschtein, D., Ma, M. & Berker, A. N. Fully and partially frustrated simple-cubic Ising models: Landau-Ginzburg-Wilson theory. Physical Review B 30, 1362–1365 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.30.1362. [9] Sachdev, S. Quantum phase transitions. Physics world 12, 33 (1999). [10] Jalabert, R. A. & Sachdev, S. Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model. Physical Review B 44, 686–690 (1991). URL https://link.aps.org/doi/10.1103/PhysRevB.44.686. [11] Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Sachdev, S. Quantum phase transitions. Physics world 12, 33 (1999). [10] Jalabert, R. A. & Sachdev, S. Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model. Physical Review B 44, 686–690 (1991). URL https://link.aps.org/doi/10.1103/PhysRevB.44.686. [11] Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Jalabert, R. A. & Sachdev, S. Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model. Physical Review B 44, 686–690 (1991). URL https://link.aps.org/doi/10.1103/PhysRevB.44.686. [11] Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014).
- Orderings of a stacked frustrated triangular system in three dimensions. Physical Review B 29, 5250–5252 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.29.5250. [8] Blankschtein, D., Ma, M. & Berker, A. N. Fully and partially frustrated simple-cubic Ising models: Landau-Ginzburg-Wilson theory. Physical Review B 30, 1362–1365 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.30.1362. [9] Sachdev, S. Quantum phase transitions. Physics world 12, 33 (1999). [10] Jalabert, R. A. & Sachdev, S. Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model. Physical Review B 44, 686–690 (1991). URL https://link.aps.org/doi/10.1103/PhysRevB.44.686. [11] Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Blankschtein, D., Ma, M. & Berker, A. N. Fully and partially frustrated simple-cubic Ising models: Landau-Ginzburg-Wilson theory. Physical Review B 30, 1362–1365 (1984). URL https://link.aps.org/doi/10.1103/PhysRevB.30.1362. [9] Sachdev, S. Quantum phase transitions. Physics world 12, 33 (1999). [10] Jalabert, R. A. & Sachdev, S. Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model. Physical Review B 44, 686–690 (1991). URL https://link.aps.org/doi/10.1103/PhysRevB.44.686. [11] Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Sachdev, S. Quantum phase transitions. Physics world 12, 33 (1999). [10] Jalabert, R. A. & Sachdev, S. Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model. Physical Review B 44, 686–690 (1991). URL https://link.aps.org/doi/10.1103/PhysRevB.44.686. [11] Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Jalabert, R. A. & Sachdev, S. Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model. Physical Review B 44, 686–690 (1991). URL https://link.aps.org/doi/10.1103/PhysRevB.44.686. [11] Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. 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[30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. 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The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. 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Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. 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Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Sachdev, S. Quantum phase transitions. Physics world 12, 33 (1999). [10] Jalabert, R. A. & Sachdev, S. Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model. Physical Review B 44, 686–690 (1991). URL https://link.aps.org/doi/10.1103/PhysRevB.44.686. [11] Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Jalabert, R. A. & Sachdev, S. Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model. Physical Review B 44, 686–690 (1991). URL https://link.aps.org/doi/10.1103/PhysRevB.44.686. [11] Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014).
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URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Jalabert, R. A. & Sachdev, S. Spontaneous alignment of frustrated bonds in an anisotropic, three-dimensional Ising model. Physical Review B 44, 686–690 (1991). URL https://link.aps.org/doi/10.1103/PhysRevB.44.686. [11] Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. 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D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. 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Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. 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[30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. 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The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. 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Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. 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Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Moessner, R., Sondhi, S. L. & Chandra, P. Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014).
- Two-Dimensional Periodic Frustrated Ising Models in a Transverse Field. Physical Review Letters 84, 4457–4460 (2000). URL https://link.aps.org/doi/10.1103/PhysRevLett.84.4457. [12] Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Isakov, S. V. & Moessner, R. Interplay of quantum and thermal fluctuations in a frustrated magnet. Physical Review B 68, 104409 (2003). URL https://link.aps.org/doi/10.1103/PhysRevB.68.104409. [13] Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. 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Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. 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Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). 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Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. 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[30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. 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The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). 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Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Villain, J. Spin glass with non-random interactions. Journal of Physics C: Solid State Physics 10, 1717 (1977). [14] King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Observation of topological phenomena in a programmable lattice of 1,800 qubits. Nature 560, 456–460 (2018). URL https://www.nature.com/articles/s41586-018-0410-x. [15] Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014).
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Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014).
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Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Kosterlitz, J. & Thouless, D. Ordering, metastability and phase transitions in two-dimensional systems 1973. J. Phys.: Condens. Matter 6, 1181 (1973). [16] King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. 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D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. 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Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. 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The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. 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The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). 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Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014).
- King, A. D. et al. Scaling advantage over path-integral Monte Carlo in quantum simulation of geometrically frustrated magnets. Nature Communications 12, 1113 (2021). URL https://www.nature.com/articles/s41467-021-20901-5http://www.nature.com/articles/s41467-021-20901-5. [17] Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Bauza, H. M. & Lidar, D. A. Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014).
- Scaling advantage in approximate optimization with quantum annealing (2024). 2401.07184. [18] King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Coherent quantum annealing in a programmable 2,000 qubit Ising chain. Nature Physics 18, 1324–1328 (2022). URL http://arxiv.org/abs/2202.05847https://www.nature.com/articles/s41567-022-01741-6. [19] Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. 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Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). 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Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. 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[30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. 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URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. 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Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. 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Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Kibble, T. W. Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General 9, 1387 (1976). [20] Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014).
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D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zurek, W. H. Cosmological experiments in superfluid helium? Nature 317, 505–508 (1985). [21] Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014).
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[26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014).
- Keesling, A. et al. Quantum kibble–zurek mechanism and critical dynamics on a programmable rydberg simulator (2019). URL http://dx.doi.org/10.1038/s41586-019-1070-1. [22] Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Ebadi, S. et al. Quantum phases of matter on a 256-atom programmable quantum simulator (2021). URL http://dx.doi.org/10.1038/s41586-021-03582-4. [23] King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014).
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Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). King, A. D. et al. Quantum critical dynamics in a 5000-qubit programmable spin glass. Nature 1–41 (2022). URL http://arxiv.org/abs/2207.13800. [24] Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014).
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The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Schumm, G., Shao, H., Guo, W., Mila, F. & Sandvik, A. W. Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014).
- Primary and secondary order parameters in the fully frustrated transverse field ising model on the square lattice (2023). 2309.02407. [25] Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Liang, S. & Pang, H. Approximate diagonalization using the density matrix renormalization-group method: A two-dimensional-systems perspective. Phys. Rev. B 49, 9214–9217 (1994). URL https://link.aps.org/doi/10.1103/PhysRevB.49.9214. [26] Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014).
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[34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Stoudenmire, E. M. & White, S. R. Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. 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Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014).
- Studying two-dimensional systems with the density matrix renormalization group. Annu. Rev. Condens. Matter Phys. 3, 111–128 (2012). [27] Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Yurke, B., Pargellis, A. N., Kovacs, T. & Huse, D. A. Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014).
- Coarsening dynamics of the xy model. Phys. Rev. E 47, 1525–1530 (1993). URL https://link.aps.org/doi/10.1103/PhysRevE.47.1525. [28] Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014).
- Arh, T. et al. The Ising triangular-lattice antiferromagnet neodymium heptatantalate as a quantum spin liquid candidate 21, 416–422. URL https://www.nature.com/articles/s41563-021-01169-y. [29] Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Li, H. et al. Kosterlitz-Thouless melting of magnetic order in the triangular quantum Ising material TmMgGaO4 11, 1111. URL https://doi.org/10.1038/s41467-020-14907-8. [30] Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Chern, K., Boothby, K., Raymond, J., Farré, P. & King, A. D. Tutorial: Calibration refinement in quantum annealing (2023). 2304.10352. [31] Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). 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Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. 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URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). 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Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Fishman, M., White, S. R. & Stoudenmire, E. M. The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. 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K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014).
- The ITensor Software Library for Tensor Network Calculations. SciPost Phys. Codebases 4 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4. [32] Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Fishman, M., White, S. R. & Stoudenmire, E. M. Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014).
- Codebase release 0.3 for ITensor. SciPost Phys. Codebases 4–r0.3 (2022). URL https://scipost.org/10.21468/SciPostPhysCodeb.4-r0.3. [33] Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zhu, Z. & White, S. R. Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014).
- Spin liquid phase of the s=12J1−J2𝑠12subscript𝐽1subscript𝐽2s=\frac{1}{2}\phantom{\rule{4.0pt}{0.0pt}}{J}_{1}-{J}_{2}italic_s = divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_J start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT - italic_J start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT heisenberg model on the triangular lattice. Phys. Rev. B 92, 041105 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.92.041105. [34] Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B. & Verstraete, F. Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014).
- Unifying time evolution and optimization with matrix product states. Phys. Rev. B 94, 165116 (2016). URL https://link.aps.org/doi/10.1103/PhysRevB.94.165116. [35] Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E. & Pollmann, F. Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014).
- Time-evolving a matrix product state with long-ranged interactions. Phys. Rev. B 91, 165112 (2015). URL https://link.aps.org/doi/10.1103/PhysRevB.91.165112. [36] Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014). Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A. LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014).
- LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python. Zenodo (2014).
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