Charge stripes due to electron correlations in the two-dimensional spinless Falicov-Kimball model

TL;DR

This study maps the ground-state phase diagram of the two-dimensional Falicov-Kimball model, revealing the emergence of stripe phases and their relation to electron correlations, with implications for understanding similar phenomena in the Hubbard model.

Contribution

It provides a comprehensive restricted phase diagram for the 2D Falicov-Kimball model, identifying stable phases and elucidating stripe formation mechanisms.

Findings

Approximately 100 stable phases identified.

Stripe phases occur in specific electron density regimes.

Relations drawn between Falicov-Kimball and Hubbard models.

Abstract

We calculate the restricted phase diagram for the Falicov-Kimball model on a two-dimensional square lattice. We consider the limit where the conduction electron density is equal to the localized electron density, which is the limit related to the S_z=0 states of the Hubbard model. After considering over 20,000 different candidate phases (with a unit cell of 16 sites or less) and their thermodynamic mixtures, we find only about 100 stable phases in the ground-state phase diagram. We analyze these phases to describe where stripe phases occur and relate these discoveries to the physics behind stripe formation in the Hubbard model.