RIGOROUS BOUNDS FOR GROUND-STATE PROPERTIES OF CORRELATED FERMI SYSTEMS

We show that upper and lower bounds on the ground-state energy of models describing correlated Fermi systems may be combined to produce bounds on the ground-state magnetization and chemical potential. Such bounds are obtainable through standard variational techniques and through recently developed methods involving exact diagonalization of finite-size clusters. For the Hubbard model on the square lattice, we give rigorous bounds for the magnetization at nonzero magnetic field B and for the chemical potential at nonzero hole density 1 - n. The quality of these bounds degrades as B --> 0 and n --> 1, precluding rigorous statements about the stability of the ferromagnetic state or the existence of a Mott-Hubbard gap. Nevertheless, the tendency towards large-U ferromagnetism and localization is evident. We discuss ways of improving these bounds, including the use of kinetic frustration, nonuniform clusters and averaging over boundary conditions.