The one-dimensional Long-Range Falikov-Kimball Model: Thermal Phase Transition and Disorder-Free Localisation

TL;DR

This paper investigates a one-dimensional long-range Falikov-Kimball model, revealing a complex phase diagram with thermal phase transitions and disorder-free localization phenomena, using advanced Monte Carlo simulations.

Contribution

It introduces a generalized 1D Falikov-Kimball model with long-range interactions and maps its phase diagram, highlighting disorder-free localization effects.

Findings

Rich phase diagram with charge density wave transitions

Fermionic localization only occurs at very large system sizes

Comparison with Anderson model confirms localization behavior

Abstract

Disorder or interactions can turn metals into insulators. One of the simplest settings to study this physics is given by the Falikov-Kimball model, which describes itinerant fermions interacting with a classical Ising background field. Despite the translational invariance of the model, inhomogenous configurations of the background field give rise to effective disorder physics which lead to a rich phase diagram in two (or more) dimensions with finite temperature charge density wave (CDW) transitions and interaction-tuned Anderson versus Mott localized phases. Here, we propose a generalised Falikov-Kimball model in one dimension with long-range interactions which shows a similarly rich phase diagram. We use an exact Markov Chain Monte Carlo method to map the phase diagram and compute the energy resolved localisation properties of the fermions. We compare the behaviour of this transitionally invariant model to an Anderson model of uncorrelated binary disorder about a background CDW field which confirms that the fermionic sector only fully localizes for very large system sizes.