Scaling up the transcorrelated density matrix renormalization group

TL;DR

This paper advances the transcorrelated density matrix renormalization group method, enabling large-scale 2D Fermi-Hubbard model calculations with improved accuracy and efficiency through technical innovations in MPO construction, entanglement exploitation, and parameter optimization.

Contribution

The authors develop novel techniques for transcorrelated DMRG, allowing for larger system sizes and significantly improved ground-state energy accuracy compared to standard methods.

Findings

Successfully applied to 12x12 lattice systems, four times larger than previous studies.

Achieved 3x to 17x reduction in energy error over standard DMRG.

Demonstrated the effectiveness of the new methods across different system types.

Abstract

Explicitly correlated methods, such as the transcorrelated method which shifts a Jastrow or Gutzwiller correlator from the wave function to the Hamiltonian, are designed for high-accuracy calculations of electronic structures, but their application to larger systems has been hampered by the computational cost. We develop improved techniques for the transcorrelated density matrix renormalization group (DMRG), in which the ground state of the transcorrelated Hamiltonian is represented as a matrix product state (MPS), and demonstrate large-scale calculations of the ground-state energy of the two-dimensional Fermi-Hubbard model. Our developments stem from three technical inventions: (i) constructing matrix product operators (MPO) of transcorrelated Hamiltonians with low bond dimension and high sparsity, (ii) exploiting the entanglement structure of the ground states to increase the accuracy of the MPS representation, and (iii) optimizing the non-linear parameter of the Gutzwiller correlator to mitigate the non-variational nature of the transcorrelated method. We examine systems of size up to $12 \times 12$ lattice sites, four times larger than previous transcorrelated DMRG studies, and demonstrate that transcorrelated DMRG yields significant improvements over standard non-transcorrelated DMRG for equivalent computational effort. Transcorrelated DMRG reduces the error of the ground state energy by $3\times$-$17 \times$, with the smallest improvement seen for a small system at half-filling and the largest improvement in a dilute closed-shell system.