# Comparison Between the f-Electron and Conduction-Electron Density of States in the Falicov-Kimball Model at Low Temperature

## TL;DR

This paper investigates whether the spectral gap at low temperature is the same for f-electrons and conduction electrons in the Falicov-Kimball model, finding strong evidence that they are indeed identical.

## Contribution

The study provides new insights into the low-temperature spectral properties of the Falicov-Kimball model, specifically comparing the electron densities of states.

## Key findings

- Spectral gaps for f-electrons and conduction electrons are the same as temperature approaches zero.
- The f-electron density of states exhibits an orthogonality catastrophe singularity in the metallic phase.
- The f-electron density of states is gapped in the insulating phase.

## Abstract

The spinless Falicov-Kimball model is one of the simplest models of many-body physics. While the conduction-electron density of states is temperature independent in the normal state, the f-electron density of states is strongly temperature dependent---it has an orthogonality catastrophe singularity in the metallic phase and is gapped in the insulating phase. The question we address here is whether the spectral gap is the same for both electron species as T->0. We find strong evidence to indicate that the answer is affirmative.