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

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.

12 pages, 11 figures

References in corpus (5)

• Non-local Adiabatic Response of a Localized System to Local Manipulations
• Critical metal-insulator transition and divergence in a two-particle irreducible vertex in disordered and interacting electron systems
• Soft Hubbard gaps in disordered itinerant models with short-range interaction
• Diagrammatic self-consistent theory of Anderson localization for the tight-binding model
• Quantum criticality at the Anderson transition: a TMT perspective

Cited by in corpus (11)

• Interpretable and unsupervised phase classification
• Extended Falicov-Kimball model: Exact solution for finite temperatures
• Extended Falicov-Kimball model: exact solution for the ground state
• Gapless regime in the charge density wave phase of the finite dimensional Falicov-Kimball model
• Universal dielectric response across a continuous metal-insulator transition
• Quantum critical magneto-transport at a continuous metal-insulator transition
• Gutzwiller projection for exclusion of holes: Application to strongly correlated Ionic Hubbard Model and Binary Alloys
• Electronic transport through correlated electron systems with nonhomogeneous charge orderings
• Thermal transport across a continuous metal-insulator transition
• Unsupervised Machine Learning Phase Classification for Falicov-Kimball Model
• Quantum critical scaling of the conductivity tensor at the metal-insulator transition in Nb${}_{1-x}$Ti${}_x$N