Conductivity of interacting spinless fermion systems via the high dimensional approach

TL;DR

This paper develops a high-dimensional approach to study the conductivity of interacting spinless fermion systems, revealing persistent conductivity at zero temperature and detailed features of the charge density wave state.

Contribution

It introduces a non-perturbative diagrammatic method based on inverse lattice dimension to analyze fermion interactions and conductivity in high dimensions.

Findings

Calculated the AB-CDW order parameter in three dimensions.

Identified two peaks in the conductivity spectrum within the energy gap.

Found that DC conductivity remains finite as temperature approaches zero.

Abstract

Spinless fermions with repulsion are treated non-perturbatively by classifying the diagrams of the generating functional $\Phi$ in powers of the inverse lattice dimension $1/d$. The equations derived from the first two orders are evaluated on the one- and on the two-particle level. The order parameter of the AB-charge density wave (AB-CDW) occurring at larger interaction is calculated in $d=3$. The Bethe-Salpeter equation is evaluated for the conductivity $\sigma(\om)$ which is found to have two peaks within the energy gap $2\Delta$ in the AB-CDW: a remnant of the Drude peak and an excitonic resonance. Unexpectedly, $\sigma_{\rm\scriptscriptstyle DC}$ does not vanish for $T\to 0$