Conductivity in a symmetry broken phase: Spinless fermions with $1/d$ corrections

TL;DR

This paper investigates the dynamic conductivity of spinless fermions in a charge density wave phase using a high-dimensional expansion, revealing a finite dc-conductivity at zero temperature and an excitonic resonance within the energy gap.

Contribution

It introduces a $1/d$ expansion approach to calculate conductivity in a symmetry broken phase, including finite dimensional effects and vertex corrections.

Findings

dc-conductivity remains finite at T=0 in the CDW phase

energy gap is visible in the dynamic conductivity

vertex corrections produce an excitonic resonance within the gap

Abstract

The dynamic conductivity $\sigma(\omega)$ of strongly correlated electrons in a symmetry broken phase is investigated in the present work. The model considered consists of spinless fermions with repulsive interaction on a simple cubic lattice. The investigated symmetry broken phase is the charge density wave (CDW) with wave vector $Q=(\pi,\pi,\pi)^\dagger$ which occurs at half-filling. The calculations are based on the high dimensional approach, i.e. an expansion in the inverse dimension $1/d$ is used. The finite dimensionality is accounted for by the inclusion of linear terms in $1/d$ and the true finite dimensional DOS. Special care is paid to the setup of a conserving approximation in the sense of Baym/Kadanoff without inconsistencies. The resulting Bethe-Salpeter equation is solved for the dynamic conductivity in the non symmetry broken and in the symmetry broken phase (AB-CDW). The dc-conductivity is reduced drastically in the CDW. Yet it does not vanish in the limit $T \to 0$ due to a subtle cancellation of diverging mobility and vanishing DOS. In the dynamic conductivity $\sigma(\omega)$ the energy gap induced by the symmetry breaking is clearly discernible. In addition, the vertex corrections of order $1/d$ lead to an excitonic resonance lying within the gap.