Phase Separation and Charge-Ordered Phases of the d = 3 Falicov-Kimball Model at T>0: Temperature-Density-Chemical Potential Global Phase Diagram from Renormalization-Group Theory

TL;DR

This paper maps the comprehensive phase diagram of the three-dimensional Falicov-Kimball model at finite temperature using renormalization-group theory, revealing multiple charge-ordered and disordered phases with complex boundary behaviors.

Contribution

It provides the first detailed global phase diagram of the 3D Falicov-Kimball model at T>0, including phase boundaries, coexistence regions, and topological cross-sections.

Findings

Five distinct phases identified, including four charge-ordered phases.

Phase boundaries include second-order and first-order transitions with critical endpoints.

Ten different phase diagram topologies across parameter space.

Abstract

The global phase diagram of the spinless Falicov-Kimball model in d = 3 spatial dimensions is obtained by renormalization-group theory. This global phase diagram exhibits five distinct phases. Four of these phases are charge-ordered (CO) phases, in which the system forms two sublattices with different electron densities. The CO phases occur at and near half filling of the conduction electrons for the entire range of localized electron densities. The phase boundaries are second order, except for the intermediate and large interaction regimes, where a first-order phase boundary occurs in the central region of the phase diagram, resulting in phase coexistence at and near half filling of both localized and conduction electrons. These two-phase or three-phase coexistence regions are between different charge-ordered phases, between charge-ordered and disordered phases, and between dense and dilute disordered phases. The second-order phase boundaries terminate on the first-order phase transitions via critical endpoints and double critical endpoints. The first-order phase boundary is delimited by critical points. The cross-sections of the global phase diagram with respect to the chemical potentials and densities of the localized and conduction electrons, at all representative interactions strengths, hopping strengths, and temperatures, are calculated and exhibit ten distinct topologies.