Momentum distribution of itinerant electrons in the one-dimensional Falicov-Kimball model

TL;DR

This study calculates the momentum distribution of itinerant electrons in the one-dimensional Falicov-Kimball model, revealing smooth distributions in periodic phases and discontinuities in phase-separated states, with unique features at specific wave vectors.

Contribution

It provides detailed analysis of $n_k$ across various ground states, highlighting the absence of Fermi surface discontinuities in periodic phases and identifying Fermi-liquid-like behavior in phase-separated states.

Findings

Smooth $n_k$ in periodic phases with no Fermi surface discontinuity

Local maximum of $n_k$ at $3k_F$ outside half-filling

Discontinuity in $n_k$ at $k=k_0$ in phase-separated states

Abstract

The momentum distribution $n_k$ of itinerant electrons in the one-dimensional Falicov-Kimball model is calculated for various ground-state phases. In particular, we examine the periodic phases with period two, three and four (that are ground-states for all Coulomb interactions) as well as the phase separated states (that are ground states for small Coulomb interactions). For all periodic phases examined the momentum distribution is a smooth function of $k$ with no sign of any discontinuity or singular behavior at the Fermi surface $k=k_F$. An unusual behavior of $n_k$ (a local maximum) is found at $k=3k_F$ for electron concentrations outside half-filling. For the phase separated ground states the momentum distribution $n_k$ exhibits discontinuity at $k=k_0 < k_F$. This behavior is interpreted in terms of a Fermi liquid.