The extended vs standard Holstein model; results in two and three dimensions

TL;DR

This paper provides numerically exact solutions for a single electron interacting with optical phonons in two and three dimensions, comparing extended and standard Holstein models and perturbative approaches, revealing limitations in effective mass reduction for realistic metals.

Contribution

It offers the first numerically exact solutions for the extended Holstein model in higher dimensions and compares them with standard models and perturbative methods.

Findings

In 2D, the effective mass remains too large for realistic metals.

In 3D, the effective mass reduction is limited to narrow coupling ranges.

Results align with earlier work on polaron effective mass behavior.

Abstract

We present numerically exact solutions to the problem of a single electron interacting through a long range interaction with optical phonons in two and three dimensions. Comparisons are made with results for the standard Holstein model, and with perturbative approaches from both the weak coupling and strong coupling sides. We find, in agreement with earlier work, that the polaron effective mass increases (decreases) in the weak (strong) coupling regime, respectively. However, in two dimensions, the decrease in effective mass still results in too large an effective mass to be relevant in realistic models of normal metals. In three dimensions the decrease can be more relevant, but exists only over a very limited range of coupling strengths.