Holstein polaron in two and three dimensions by quantum Monte Carlo

TL;DR

This paper extends a quantum Monte Carlo method to study the Holstein polaron in two and three dimensions, analyzing how temperature, size, and parameters affect polaron behavior with improved accuracy.

Contribution

It introduces an extended quantum Monte Carlo approach for higher-dimensional Holstein models, addressing sign problems and enhancing result precision.

Findings

Sign problem diminishes with increasing system size

Temperature and dimensionality significantly influence polaron crossover

Results are extrapolated to reduce Trotter discretization errors

Abstract

A recently developed quantum Monte Carlo approach to the Holstein model with one electron [PRB 69, 024301 (2004)] is extended to two and three dimensional lattices. A moderate sign problem occurs, which is found to diminish with increasing system size in all dimensions, and not to affect simulations significantly. We present an extensive study of the influence of temperature, system size, dimensionality and model parameters on the small-polaron cross over. Results are extrapolated to remove the error due to the Trotter discretization, which significantly improves the accuracy. Comparison with existing work and other quantum Monte Carlo methods is made. The method can be extended to the many-electron case.