Optical and dc transport properties of a strongly correlated charge density wave system: exact solution in the ordered phase of the spinless Falicov-Kimball model with dynamical mean-field theory

TL;DR

This paper develops an exact dynamical mean-field theory framework for analyzing optical and dc transport in an ordered charge-density-wave phase of the spinless Falicov-Kimball model, revealing anomalous behaviors and sum rule modifications.

Contribution

It provides the first exact solution for transport properties in the ordered phase of this model using dynamical mean-field theory, including detailed analysis of spectral and sum rule behaviors.

Findings

Vertex corrections vanish in the ordered phase.

Density of states and transport coefficients show anomalous behavior due to subgap states.

Total optical spectral weight varies with interaction strength.

Abstract

We derive the dynamical mean-field theory equations for transport in an ordered charge-density-wave phase on a bipartite lattice. The formalism is applied to the spinless Falicov-Kimball model on a hypercubic lattice at half filling. We determine the many-body density of states, the dc charge and heat conductivities, and the optical conductivity. Vertex corrections continue to vanish within the ordered phase, but the density of states and the transport coefficients show anomalous behavior due to the rapid development of thermally activated subgap states. We also examine the optical sum rule and sum rules for the first three moments of the Green's functions within the ordered phase and see that the total optical spectral weight in the ordered phase either decreases or increases depending on the strength of the interactions.