Mean Field Magnetic Phase Diagrams for the Two Dimensional t — t′ — U Hubbard Model

We study the ground state phase diagram of the two dimensional t — t′ — U Hubbard model concentrating on the competition between antiferro-, ferro-, and paramagnetism. It is known that unrestricted Hartree–Fock- and quantum Monte Carlo calculations for this model predict inhomogeneous states in large regions of the parameter space. Standard mean field theory, i.e., Hartree–Fock theory restricted to homogeneous states, fails to produce such inhomogeneous phases. We show that a generalization of the mean field method to the grand canonical ensemble circumvents this problem and predicts inhomogeneous states, represented by mixtures of homogeneous states, in large regions of the parameter space. We present phase diagrams which differ considerably from previous mean field results but are consistent with, and extend, results obtained with more sophisticated methods.