Finite-Temperature Variational Monte Carlo Method for Strongly Correlated Electron Systems

TL;DR

This paper introduces a finite-temperature variational Monte Carlo method for strongly correlated electrons, extending ground-state techniques to higher temperatures by optimizing a truncated Hilbert space, enabling larger system simulations without the sign problem.

Contribution

The paper develops a novel finite-temperature variational Monte Carlo approach using the TDVP, allowing larger system sizes and avoiding the sign problem in strongly correlated electron systems.

Findings

Accurately reproduces finite-temperature properties of Hubbard models

Demonstrates efficiency and scalability for large systems

Provides a new framework for thermal state simulation

Abstract

A new computational method for finite-temperature properties of strongly correlated electrons is proposed by extending the variational Monte Carlo method originally developed for the ground state. The method is based on the path integral in the imaginary-time formulation, starting from the infinite-temperature state that is well approximated by a small number of certain random initial states. Lower temperatures are progressively reached by the imaginary-time evolution. The algorithm follows the framework of the quantum transfer matrix and finite-temperature Lanczos methods, but we extends them to treat much larger system sizes without the negative sign problem by optimizing the truncated Hilbert space on the basis of the time-dependent variational principle (TDVP). This optimization algorithm is equivalent to the stochastic reconfiguration (SR) method that has been frequently used for the ground state to optimally truncate the Hilbert space. The obtained finite-temperature states allow an interpretation based on the thermal pure quantum (TPQ) state instead of the conventional canonical-ensemble average. Our method is tested for the one- and two-dimensional Hubbard models and its accuracy and efficiency are demonstrated.