Real-space cluster dynamical mean-field approach to the Falicov-Kimball model: An alloy-analogy approach

TL;DR

This paper develops a real-space cluster dynamical mean-field approach to study the Falicov-Kimball model, revealing novel localization phenomena and non-analyticities in two-particle vertices that signal a new type of strong localization.

Contribution

It introduces an analytic cluster extension that captures intra-cluster correlations in the Falicov-Kimball model, highlighting non-analyticities and localization effects beyond traditional approximations.

Findings

Identification of non-analyticities in two-particle vertices before band-splitting transition

Observation of a transition in wave function overlap from power-law to anomalous behavior

Evidence of a novel strong localization in the Falicov-Kimball model

Abstract

It is long known that the best single-site coherent potential approximation (CPA) falls short of describing Anderson localization (AL). Here, we study a binary alloy disorder (or equivalently, a spinless Falicov-Kimball (FK)) model and construct a dominantly analytic cluster extension that treats intra-cluster ($1/d$, $d$=spatial dimension) correlations exactly. We find that, in general, the irreducible two-particle vertex exhibits clear non-analyticities before the band-splitting transition of the Hubbard type occurs, signaling onset of an unusual type of localization at strong coupling. Using time-dependent response to a sudden local quench as a diagnostic, we find that the long-time wave function overlap changes from a power-law to an anomalous form at strong coupling, lending additional support to this idea. Our results also imply such novel "strong" localization in the equivalent FK model, the simplest interacting fermion system.