The spectral properties of the Falicov-Kimball model in the weak-coupling limit

TL;DR

This paper investigates the spectral properties of the one-dimensional Falicov-Kimball model in the weak-coupling limit, revealing how energy gaps behave differently with zero and finite hybridization, impacting understanding of insulator-metal transitions.

Contribution

It provides a detailed analysis of the electron density of states and energy gaps in the Falicov-Kimball model, highlighting the effects of hybridization on spectral behavior.

Findings

At zero hybridization, gaps do not coincide and the activation gap vanishes discontinuously.

At finite hybridization, all gaps coincide and vanish continuously at the transition.

The results have implications for modeling real materials with similar electronic properties.

Abstract

The $f$ and $d$ electron density of states of the one-dimensional Falicov-Kimball model are studied in the weak-coupling limit by exact diagonalization calculations. The resultant behaviors are used to examine the $d$-electron gap ($\Delta_{d}$), the $f$-electron gap ($\Delta_{f}$), and the $fd$-electron gap ($\Delta_{fd}$) as functions of the $f$-level energy $E_f$ and hybridization $V$. It is shown that the spinless Falicov-Kimball model behaves fully differently for zero and finite hybridization between $f$ and $d$ states. At zero hybridization the energy gaps do not coincide ($\Delta_{d}\neq \Delta_{f} \neq \Delta_{fd}$), and the activation gap $\Delta_{fd}$ vanishes discontinuously at some critical value of the $f$-level energy $E_{fc}$. On the other hand, at finite hybridization all energy gaps coincide and vanish continuously at the insulator-metal transition point $E_f=E_{fc}$. The importance of these results for a description of real materials is discussed.