Comparing scattering rates from Boltzmann and dynamical mean-field theory

TL;DR

This paper compares electron scattering rates in the 2D Hubbard model using Boltzmann and dynamical mean-field theory, revealing differences in weak and strong interaction regimes and highlighting the limitations of Boltzmann approaches for Mott insulators.

Contribution

It provides a detailed comparison of scattering rates from BSE and DMFT, including an intermediate BSE without momentum conservation, across different interaction regimes.

Findings

BSE and DMFT agree well for band insulators at weak interactions.

BSE with momentum conservation shows larger scattering rates and momentum differentiation.

DMFT predicts much larger scattering rates for Mott insulators, beyond BSE's scope.

Abstract

We compute scattering rates for electrons in the two-dimensional Hubbard model for a one-orbital metal and a two-orbital band insulator by means of the Boltzmann scattering equation (BSE) and dynamical mean-field theory (DMFT). As an intermediate method between both, we also consider the BSE without momentum conservation. In the weak interaction regime and for the band insulator, the last two agree to very good accuracy. The BSE with momentum conservation, on the other hand, shows slightly larger scattering rates, and a momentum differentiation of these on the Fermi surface. For the Mott insulator at strong interaction, the DMFT electron scattering rates are much larger and defy a BSE description. Noteworthy, the scattering rates for the band insulator are exceedingly small because -- in contrast to the Mott insulator -- there is virtually no impact ionization.