Papers
Topics
Authors
Recent
Search
2000 character limit reached

Massive Higher-Spin Fields in the Fractional Quantum Hall Effect

Published 24 Apr 2024 in cond-mat.str-el, cond-mat.mes-hall, and hep-th | (2404.16013v2)

Abstract: Incompressibility plays a key role in the geometric description of fractional quantum Hall fluids. It is naturally related to quantum area-preserving diffeomorphisms and the underlying Girvin-MacDonald-Plazman algebra, which gives rise to an emergent non-relativistic massive spin-2 mode propagating in the bulk. The corresponding metric tensor can be identified with a nematic order parameter for the bulk states. In the linearised regime with a flat background, it has been shown that this mode can be described by a spin-2 Schroedinger action. However, quantum area-preserving diffeomorphisms also suggest the existence of higher-spin modes that cannot be described through nematic fractional quantum Hall states. Here, we consider p-atic Hall phases, in which the corresponding p-atic order parameters are related to higher-rank symmetric tensors. We then show that in this framework, non-relativistic massive chiral higher-spin fields naturally emerge and that their dynamics is described by higher-spin Schroedinger actions. We finally show that these effective actions can be derived from relativistic massive higher-spin theories in 2+1 dimensions after taking a non-relativistic limit.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (63)
  1. J. R. Schrieffer, Theory of superconductivity (CRC press, 2018).
  2. P. de Gennes and J. Prost, The Physics of Liquid Crystals, International Series of Monographs on Physics (Clarendon Press, 1993).
  3. J. K. Pachos, Introduction to topological quantum computation (Cambridge University Press, 2012).
  4. X.-G. Wen, Colloquium: Zoo of quantum-topological phases of matter, Rev. Mod. Phys. 89, 041004 (2017).
  5. X.-G. Wen, Topological orders and edge excitations in fractional quantum Hall states, Advances in Physics 44, 405 (1995).
  6. X.-L. Qi and S.-C. Zhang, Topological insulators and superconductors, Rev. Mod. Phys. 83, 1057 (2011).
  7. M. Z. Hasan and C. L. Kane, Colloquium: Topological insulators, Rev. Mod. Phys. 82, 3045 (2010).
  8. A. Y. Kitaev, Unpaired Majorana fermions in quantum wires, Physics-uspekhi 44, 131 (2001).
  9. P. Maraner, J. K. Pachos, and G. Palumbo, Specific heat of 2D interacting Majorana fermions from holography, Scientific Reports 9, 17308 (2019).
  10. L. Radzihovsky and A. T. Dorsey, Theory of quantum Hall nematics, Phys. Rev. Lett. 88, 216802 (2002).
  11. M. Mulligan, C. Nayak, and S. Kachru, Effective field theory of fractional quantized Hall nematics, Phys. Rev. B 84, 195124 (2011).
  12. Y. You, G. Y. Cho, and E. Fradkin, Theory of nematic fractional quantum Hall states, Phys. Rev. X 4, 041050 (2014).
  13. F. D. M. Haldane, Geometrical description of the fractional quantum Hall effect, Phys. Rev. Lett. 107, 116801 (2011).
  14. S. Golkar, D. X. Nguyen, and D. T. Son, Spectral sum rules and magneto-roton as emergent graviton in fractional quantum Hall effect, Journal of High Energy Physics 2016, 21 (2016a).
  15. A. Gromov, S. D. Geraedts, and B. Bradlyn, Investigating anisotropic quantum Hall states with bimetric geometry, Phys. Rev. Lett. 119, 146602 (2017).
  16. A. Gromov and D. T. Son, Bimetric theory of fractional quantum Hall states, Phys. Rev. X 7, 041032 (2017).
  17. A. Cappelli, C. A. Trugenberger, and G. R. Zemba, Infinite symmetry in the quantum Hall effect, Nuclear Physics B 396, 465 (1993).
  18. B. Oblak and B. Estienne, Adiabatic deformations of quantum Hall droplets, SciPost Phys. 15, 159 (2023).
  19. G. Palumbo, Noncommutative geometry and deformation quantization in the quantum Hall fluids with inhomogeneous magnetic fields, Journal of Physics A: Mathematical and Theoretical 56, 455203 (2023).
  20. S. M. Girvin, A. H. MacDonald, and P. M. Platzman, Magneto-roton theory of collective excitations in the fractional quantum Hall effect, Phys. Rev. B 33, 2481 (1986).
  21. E. Bergshoeff, M. P. Blencowe, and K. S. Stelle, Area Preserving Diffeomorphisms and Higher Spin Algebra, Commun. Math. Phys. 128, 213 (1990).
  22. A. Cappelli and E. Randellini, Multipole expansion in the quantum Hall effect, Journal of High Energy Physics 2016, 105 (2016).
  23. Z. Liu, A. Gromov, and Z. Papić, Geometric quench and nonequilibrium dynamics of fractional quantum Hall states, Phys. Rev. B 98, 155140 (2018).
  24. M. F. Lapa, A. Gromov, and T. L. Hughes, Geometric quench in the fractional quantum Hall effect: Exact solution in quantum Hall matrix models and comparison with bimetric theory, Phys. Rev. B 99, 075115 (2019).
  25. F. D. M. Haldane, Two-dimensional inversion symmetry as the fundamental symmetry of incompressible quantum Hall fluids (2023), arXiv:2302.10968 [cond-mat.mes-Hall] .
  26. L. Giomi, J. Toner, and N. Sarkar, Hydrodynamic theory of p𝑝pitalic_p-atic liquid crystals, Phys. Rev. E 106, 024701 (2022a).
  27. L. Giomi, J. Toner, and N. Sarkar, Long-ranged order and flow alignment in sheared p𝑝pitalic_p-atic liquid crystals, Phys. Rev. Lett. 129, 067801 (2022b).
  28. T. C. Lubensky and L. Radzihovsky, Theory of bent-core liquid-crystal phases and phase transitions, Phys. Rev. E 66, 031704 (2002).
  29. M. J. Bowick and L. Giomi, Two-dimensional matter: order, curvature and defects, Advances in Physics 58, 449 (2009).
  30. L. Balents, Spatially ordered fractional quantum Hall states, Europhysics Letters 33, 291 (1996).
  31. K. Musaelian and R. Joynt, Broken rotation symmetry in the fractional quantum Hall system, Journal of Physics: Condensed Matter 8, L105 (1996).
  32. E. Fradkin and S. A. Kivelson, Liquid-crystal phases of quantum Hall systems, Phys. Rev. B 59, 8065 (1999).
  33. M. M. Fogler, Quantum Hall liquid crystals, International Journal of Modern Physics B 16, 2924 (2002).
  34. C. Wexler and O. Ciftja, Novel liquid crystalline phases in quantum Hall systems, International Journal of Modern Physics B 20, 747 (2006).
  35. E. G. Virga, Octupolar order in two dimensions, The European Physical Journal E 38, 63 (2015).
  36. E. A. Bergshoeff, J. Rosseel, and P. K. Townsend, Gravity and the Spin-2 Planar Schrödinger Equation, Phys. Rev. Lett. 120, 141601 (2018).
  37. V. Bargmann, On Unitary ray representations of continuous groups, Annals Math. 59, 1 (1954).
  38. Y. M. Zinoviev, Massless spin 2 interacting with massive higher spins in d = 3, Journal of High Energy Physics 2023, 58 (2023).
  39. Y. M. Zinoviev, On massive high spin particles in (A)dS (2001), arXiv:hep-th/0108192 .
  40. Y. M. Zinoviev, Frame-like gauge invariant formulation for massive high spin particles, Nucl. Phys. B 808, 185 (2009).
  41. E. D. Skvortsov and M. A. Vasiliev, Transverse Invariant Higher Spin Fields, Phys. Lett. B 664, 301 (2008).
  42. A. Campoleoni and D. Francia, Maxwell-like lagrangians for higher spins, Journal of High Energy Physics 2013, 168 (2013).
  43. F. Ferrari and S. Klevtsov, FQHE on curved backgrounds, free fields and large N, Journal of High Energy Physics 2014, 86 (2014).
  44. S. Klevtsov and P. Wiegmann, Geometric adiabatic transport in quantum Hall states, Phys. Rev. Lett. 115, 086801 (2015).
  45. T. Can, M. Laskin, and P. Wiegmann, Fractional quantum Hall effect in a curved space: Gravitational anomaly and electromagnetic response, Phys. Rev. Lett. 113, 046803 (2014).
  46. P. Salgado-Rebolledo and G. Palumbo, Extended Nappi-Witten geometry for the fractional quantum Hall effect, Phys. Rev. D 103, 125006 (2021).
  47. E. Bergshoeff, J. Rosseel, and T. Zojer, Non-relativistic fields from arbitrary contracting backgrounds, Class. Quant. Grav. 33, 175010 (2016).
  48. P. Salgado-Rebolledo and G. Palumbo, Nonrelativistic supergeometry in the moore-read fractional quantum Hall state, Phys. Rev. D 106, 065020 (2022).
  49. A. Gromov, E. J. Martinec, and S. Ryu, Collective excitations at filling factor 5/2525/25 / 2: The view from superspace, Phys. Rev. Lett. 125, 077601 (2020).
  50. A. Campoleoni and S. Fredenhagen, Higher-spin gauge theories in three spacetime dimensions (2024), arXiv:2403.16567 [hep-th] .
  51. B. Chen and J. Long, High spin topologically massive gravity, Journal of High Energy Physics 2011, 114 (2011).
  52. G. Palumbo, Fractional quantum Hall effect for extended objects: from skyrmionic membranes to dyonic strings, Journal of High Energy Physics 2022, 124 (2022).
  53. T. Damour and S. Deser, ’Geometry’ of Spin 3 Gauge Theories, Ann. Inst. H. Poincare Phys. Theor. 47, 277 (1987).
  54. E. Bergshoeff, O. Hohm, and P. Townsend, On massive gravitons in 2+1 dimensions, J. Phys. Conf. Ser. 229, 012005 (2010).
  55. D. Dalmazi and A. L. R. d. Santos, Higher spin analogs of linearized topologically massive gravity and linearized new massive gravity, Phys. Rev. D 104, 085023 (2021).
  56. C. N. Pope, L. J. Romans, and X. Shen, The Complete Structure of W(Infinity), Phys. Lett. B 236, 173 (1990).
  57. M. Henneaux and S.-J. Rey, Nonlinear w∞subscript𝑤w_{\infty}italic_w start_POSTSUBSCRIPT ∞ end_POSTSUBSCRIPT as asymptotic symmetry of three-dimensional higher spin AdS gravity, Journal of High Energy Physics 2010, 7 (2010).
  58. A. Campoleoni and M. Henneaux, Asymptotic symmetries of three-dimensional higher-spin gravity: the metric approach, Journal of High Energy Physics 2015, 143 (2015).
  59. E. Bergshoeff, B. de Wit, and M. A. Vasiliev, The Structure of the super-W∞⁢(λ)subscript𝑊𝜆W_{\infty}(\lambda)italic_W start_POSTSUBSCRIPT ∞ end_POSTSUBSCRIPT ( italic_λ ) algebra, Nucl. Phys. B 366, 315 (1991).
  60. A. Dutta, Non-relativistic limit for higher spin fields and planar Schroedinger equation in 3D (2023), arXiv:2304.05321 [hep-th] .
  61. C. Fronsdal, Massless Fields with Integer Spin, Phys. Rev. D 18, 3624 (1978).
  62. S. D. Rindani and M. Sivakumar, Gauge - Invariant Description of Massive Higher - Spin Particles by Dimensional Reduction, Phys. Rev. D 32, 3238 (1985).
  63. L. P. S. Singh and C. R. Hagen, Lagrangian formulation for arbitrary spin. 1. The boson case, Phys. Rev. D 9, 898 (1974).
Citations (1)
View on Semantic Scholar

Summary

No one has generated a summary of this paper yet.

Sign Up to Summarize

Paper to Video (Beta)

No one has generated a video about this paper yet.

Sign Up to Generate All Videos Subscribe on YouTube

Whiteboard

No one has generated a whiteboard explanation for this paper yet.

Sign Up to Generate

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Generate Now

Continue Learning

We haven't generated follow-up questions for this paper yet.

Generate Now

Collections

Sign up for free to add this paper to one or more collections.

Sign Up

Tweets

Sign up for free to view the 1 tweet with 0 likes about this paper.

Sign Up for Free