Segregation in the asymmetric Hubbard model

We study the `asymmetric' Hubbard model, where hoppings of electrons depend on their spin. For strong interactions and sufficiently asymmetric hoppings, it is proved that the ground state displays phase separation away from half-filling. This extends a recent result obtained with Freericks and Lieb for the Falicov-Kimball model. It is based on estimates for the sum of lowest eigenvalues of the discrete Laplacian in arbitrary domains.