The simplified Hubbard model in one and two dimensions:Thermodynamic and dynamic properties

Thermodynamic and dynamic properties of the one and two-dimensional simplified Hubbard model are studied. At zero temperature and half filling, no metal-insulator transition occurs for nonzero coupling U and the system is an antiferromagnetic insulator. The behavior of the gap in the single-particle density of states is investigated as a function of U, temperature and band filling rho. For weak to intermediate coupling the gap at half filling closes for increasing temperatures. The ground state of doped lattices exhibits a metal-insulator transition at -4d <U(c)(rho) less-than-or-equal-to - 2d (d is the lattice dimensionality) and displays ferromagnetism without long-range order for U > U(c). The co-existence for variable temperatures and electron densities of metallic behavior and magnetic and charge-density long-range order is demonstrated. The critical temperature for long-range order is calculated for the half-filled two-dimensional case. Results for the optical conductivity and several thermodynamic properties are presented.