Ground States and Flux Configurations of the Two-dimensional Falicov-Kimball Model

TL;DR

This paper explores the ground states and flux configurations of the two-dimensional Falicov-Kimball model on square and triangular lattices, revealing new crystalline states and effects of magnetic flux, including a bosonic variant.

Contribution

It introduces new crystalline ground states for the Falicov-Kimball model and analyzes the impact of magnetic flux and flux configurations on the phase diagram.

Findings

Discovery of new crystalline ground states.

Effect of magnetic flux on phase structure.

Existence of crystalline states in a bosonic variant.

Abstract

The Falicov-Kimball model is a lattice model of itinerant spinless fermions ("electrons") interacting by an on-site potential with classical particles ("ions"). We continue the investigations of the crystalline ground states that appear for various filling of electrons and ions, for large coupling. We investigate the model for square as well as triangular lattices. New ground states are found and the effects of a magnetic flux on the structure of the phase diagram is studied. The flux phase problem where one has to find the optimal flux configurations and the nuclei configurations is also solved in some cases. Finaly we consider a model where the fermions are replaced by hard-core bosons. This model also has crystalline ground states. Therefore their existence does not require the Pauli principle, but only the on-site hard-core constraint for the itinerant particles.