Canonical Phase Diagrams of the 1-D Falicov-Kimball Model at T=0

TL;DR

This paper constructs detailed zero-temperature phase diagrams for the 1D Falicov-Kimball model, revealing new phases, structural transitions, and symmetry tendencies through numerical analysis of periodic configurations.

Contribution

It provides more detailed phase diagrams than previous studies, including new phases and insights into phase formation and symmetry in the 1D Falicov-Kimball model.

Findings

Identification of new characteristic phases like generalized homogeneous and crenel phases

Observation of a structural phase transition at certain coupling values

Detection of a tendency towards hole-particle symmetry as U decreases

Abstract

The Falicov-Kimball model of spinless quantum electrons hopping on a 1-dimensional lattice and of immobile classical ions occupying some lattice sites, with only intrasite coupling between those particles, have been studied at zero temperature by means of well-controlled numerical procedures. For selected values of the unique coupling parameter $U$ the restricted phase diagrams (based on all the periodic configurations of localized particles (ions) with period not greater than 16 lattice constants, typically) have been constructed in the grand-canonical ensemble. Then these diagrams have been translated into the canonical ensemble. Compared to the diagrams obtained in other studies our ones contain more details, in particular they give better insight into the way the mixtures of periodic phases are formed. Our study has revealed several families of new characteristic phases like the generalized most homogeneous and the generalized crenel phases, a first example of a structural phase transition and a tendency to build up an additional symmetry -- the hole-particle symmetry with respect to the ions (electrons) only, as $U$ decreases.