Coulomb Glasses: A Comparison Between Mean Field and Monte Carlo Results

TL;DR

This paper compares mean field theory and Monte Carlo simulations for Coulomb glasses, revealing discrepancies in transition rates and conductance predictions, and proposes modifications to improve mean field accuracy.

Contribution

It introduces a modified mean field rate approach that accounts for correlations, improving agreement with Monte Carlo results in Coulomb glass models.

Findings

Mean field rates underestimate important transitions.

Modified rates improve mean field predictions.

Both methods show Efros-Shklovskii behavior in conductance.

Abstract

Recently a local mean field theory for both eqilibrium and transport properties of the Coulomb glass was proposed [A. Amir et al., Phys. Rev. B 77, 165207 (2008); 80, 245214 (2009)]. We compare the predictions of this theory to the results of dynamic Monte Carlo simulations. In a thermal equilibrium state we compare the density of states and the occupation probabilities. We also study the transition rates between different states and find that the mean field rates underestimate a certain class of important transitions. We propose modified rates to be used in the mean field approach which take into account correlations at the minimal level in the sense that transitions are only to take place from an occupied to an empty site. We show that this modification accounts for most of the difference between the mean field and Monte Carlo rates. The linear response conductance is shown to exhibit the Efros-Shklovskii behaviour in both the mean field and Monte Carlo approaches, but the mean field method strongly underestimates the current at low temperatures. When using the modified rates better agreement is achieved.