Compactifying Electronic Wavefunctions I: Error-Mitigated Transcorrelated DMRG

Abstract: Transcorrelation (TC) techniques effectively enhance convergence rates in strongly correlated fermionic systems by embedding electron-electron cusp into the Jastrow factor of similarity transformations, yielding a non-Hermitian, yet iso-spectral, Hamiltonian. This non-Hermitian nature introduces significant challenges for variational methods such as the Density Matrix Renormalization Group (DMRG). To address these, existing approaches often rely on computationally expensive methods prone to errors, such as imaginary-time evolution. We introduce an Error-Mitigated Transcorrelated DMRG (EMTC-DMRG), a classical variational algorithm that overcomes these challenges by integrating existing techniques to achieve superior accuracy and efficiency. Key features of our algorithm include: (a) an analytical formulation of the transcorrelated Fermi-Hubbard Hamiltonian; (b) a numerically exact, uncompressed Matrix Product Operator (MPO) representation developed via symbolic optimization and the Hopcroft-Karp algorithm; and (c) a time-independent DMRG with a two-site sweep algorithm; (d) we use Davidson solver even for a non-Hermitian Hamiltonian. Our method significantly enhances computational efficiency and accuracy in determining ground-state energies for the two-dimensional transcorrelated Fermi-Hubbard model with periodic boundary conditions. Additionally, it can be adapted to compute both ground and excited states in molecular systems.