Quantum Monte Carlo and variational approaches to the Holstein model

TL;DR

This paper introduces an efficient quantum Monte Carlo algorithm for the Holstein model with one electron, utilizing a canonical transformation and principal component sampling to enable large-scale, accurate simulations across various parameters.

Contribution

It presents a novel, computationally efficient quantum Monte Carlo method for the Holstein model, reducing effort and enabling large-scale simulations, with potential extension to many-electron systems.

Findings

Efficient simulations for a wide range of parameters.

Good agreement with exact diagonalization results.

Applicable to many-electron cases.

Abstract

Based on the canonical Lang-Firsov transformation of the Hamiltonian we develop a very efficient quantum Monte Carlo algorithm for the Holstein model with one electron. Separation of the fermionic degrees of freedom by a reweighting of the probability distribution leads to a dramatic reduction in computational effort. A principal component representation of the phonon degrees of freedom allows to sample completely uncorrelated phonon configurations. The combination of these elements enables us to perform efficient simulations for a wide range of temperature, phonon frequency and electron-phonon coupling on clusters large enough to avoid finite-size effects. The algorithm is tested in one dimension and the data are compared with exact-diagonalization results and with existing work. Moreover, the ideas presented here can also be applied to the many-electron case. In the one-electron case considered here, the physics of the Holstein model can be described by a simple variational approach.