Polaron effective mass from Monte Carlo simulations

TL;DR

This paper introduces a novel Monte Carlo method to compute the polaron effective mass using path-integral techniques, allowing for accurate calculations across various parameters and system sizes.

Contribution

A new Monte Carlo algorithm based on path-integral representation for calculating polaron effective mass with no limitations on system parameters.

Findings

Method accurately computes effective mass in the 1D Holstein model.

No restrictions on system size or parameters, enabling broad applicability.

Requires large statistics for stable numerical results.

Abstract

A new Monte Carlo algorithm for calculating polaron effective mass is proposed. It is based on the path-integral representation of a partial partition function with fixed total quasi-momentum. Phonon degrees of freedom are integrated out analytically resulting in a single-electron system with retarded self-interaction and open boundary conditions in imaginary time. The effective mass is inversely proportional to the covariance of total energy calculated on an electron trajectory and the square distance between ends of the trajectory. The method has no limitations on values of model parameters and on the size and dimensionality of the system although large statistics is required for stable numerical results. The method is tested on the one-dimensional Holstein model for which simulation results are presented.