Some Exact Results for the Zero-Bandwidth Extended Hubbard Model with Intersite Charge and Magnetic Interactions

The extended Hubbard model in the zero-bandwidth limit is studied. The effective Hamiltonian consists of (i) on-site U interaction, (ii) intersite density-density interaction W, and (iii) Ising-like magnetic exchange interaction J between the nearest-neighbors. We present rigorous (and analytical) results obtained within the transfer-matrix method for 1D chain in two particular cases: (a) W=0 and n=1; (b) U → +∞ and n=1/2 (W ≠ 0, J ≠ 0). We obtain the exact formulae for the partition functions which enables to calculate thermodynamic properties such as entropy, specific heat (c), and double occupancy per site. In both cases the system exhibits an interesting temperature dependence of c involving a characteristic two-peak structure. There are no phase transitions at finite temperatures and the only transitions occur in the ground state.