Periodic Ground States in the Neutral Falicov-Kimball Model in Two Dimensions

摘要

We consider the Falicov-Kimball model in two dimensions in the neutral case,i.e, the number of mobile electrons is equal to the number of ions. Forrational densities between 1/3 and 2/5 we prove that the ground state isperiodic if the strength of the attraction between the ions and electrons islarge enough. The periodic ground state is given by taking the one dimensionalperiodic ground state found by Lemberger and then extending it into twodimensions in such a way that the configuration is constant along lines at a 45degree angle to the lattice directions.