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

We calculate the restricted phase diagram for the Falicov-Kimball model on a two-dimensional square lattice. We consider the limit where the average conduction electron density is equal to the average 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, where the ground state is usually the phase separated mixture of two or three stable phases, that often have different electron densities than in the Maxwell-constructed mixture. We analyze these phases to describe where stripe phases occur and relate these discoveries (were appropriate) to the physics behind stripe formation in the Hubbard model.