Extended Hubbard model at strong coupling.

Abstract

The half-filled extended Hubbard model (containing nearest-neighbor interaction) is considered at strong coupling in fourth-order perturbation theory. The ground-state energies in the spin- and charge-density-wave phases and the resulting phase diagram are calculated in various dimensions: here d=1, d=\ensuremath{\infty}, high dimensions (d\ensuremath{\gg}1), and d=2,3 are discussed separately. In d=1 it is shown that, for U\ensuremath{\gtrsim}6, fourth-order perturbation theory leads to excellent agreement with existing Monte Carlo data. Second-order perturbation theory alone is valid only at unrealistically large values of U and V. In d=\ensuremath{\infty}, one needs fourth-order perturbation theory to obtain any nontrivial contribution to the phase diagram at all. As a consequence the fourth-order corrections to the ground-state energy and to the phase diagram are large also in d=2,3. The formalism used to obtain the perturbative expansion is discussed in an appendix.