Mobility of Holstein polaron: an unbiased approach

TL;DR

This paper provides the first unbiased numerical analysis of Holstein polaron mobility in one dimension, revealing distinct conduction regimes and temperature-dependent behaviors.

Contribution

It introduces an unbiased numerical approach combining diagrammatic and world-line Monte Carlo methods to study polaron mobility in the thermodynamic limit.

Findings

Identified multiple conduction regimes in the λ-T parameter space.

Discovered mobility convergence at high temperatures across different λ values.

Provided detailed temperature and frequency dependence of polaron mobility.

Abstract

We present the first unbiased results for the mobility $\mu$ of one-dimensional Holstein polaron obtained by numerical analytic continuation combined with diagrammatic and world-line Monte Carlo methods in the thermodynamic limit. We have identified for the first time, by the characteristic $\omega$ and $T$ dependence in the wide region of parameters, several distinct regimes in the $\lambda-T$ plane including band conduction region, incoherent metallic region, activated hopping region, and high temperature saturation region. We observe for the first time that although mobilities and mean free paths at different values of $\lambda$ differ by many orders of magnitude at small temperatures, their values at $T$ larger than the bandwidth become very close to each other.