Effects of dimensionality and anisotropy on the Holstein polaron

TL;DR

This paper investigates how anisotropy and dimensionality influence polaron properties in the Holstein model using perturbation theory, with results supported by variational and quantum Monte Carlo methods.

Contribution

It provides a detailed analysis of anisotropy effects on polaron energy, self-trapping, and mass enhancement across different dimensions, combining perturbative and numerical approaches.

Findings

Anisotropy significantly affects polaron self-trapping transition.

Dimensionality influences polaron radius and mass enhancement.

Perturbative results align well with variational and Monte Carlo data.

Abstract

We apply weak-coupling perturbation theory and strong-coupling perturbation theory to the Holstein molecular crystal model in order to elucidate the effects of anisotropy on polaron properties in D dimensions. The ground state energy is considered as a primary criterion through which to study the effects of anisotropy on the self-trapping transition, the self-trapping line associated with this transition, and the adiabatic critical point. The effects of dimensionality and anisotropy on electron-phonon correlations and polaronic mass enhancement are studied, with particular attention given to the polaron radius and the characteristics of quasi-1D and quasi-2D structures. Perturbative results are confirmed by selected comparisons with variational calculations and quantum Monte Carlo data.