Optical Conductivity of the two dimensional Hubbard model: vertex corrections, emergent Galilean invariance and the accuracy of the single-site dynamical mean field approximation

TL;DR

This paper investigates the optical conductivity of the 2D Hubbard model at zero temperature, comparing second-order perturbation results with single-site dynamical mean field theory, revealing its strengths and limitations across different electron densities.

Contribution

It provides a detailed comparison between perturbative calculations and DMFT, highlighting the conditions under which DMFT remains accurate or fails.

Findings

DMFT is semi-quantitatively accurate for most densities

Fails near empty or full bands due to emergent Galilean invariance

Inaccurate near half filling when nesting effects are significant

Abstract

We compute the frequency dependent conductivity of the two dimensional square lattice Hubbard model at zero temperature as a function of density to second order in the interaction strength, and compare the results to the predictions of single-site dynamical mean field theory computed at the same order. We find that despite the neglect of vertex corrections, the single site dynamical mean field approximation produces semiquantitatively accurate results for most carrier concentrations, but fails qualitatively for the nearly empty or nearly filled band cases where the theory exhibits an emergent Galilean invariance. The theory also becomes qualitatively inaccurate very near half filling if nesting is important.