1/d corrections for interacting spinless fermions: One-particle properties

Abstract

One-particle properties of the spinless fermion model with repulsion at half filling are calculated within an approach correct to first order in the inverse of the lattice dimensiond. Continuity of the limitd→∞ requires a scaling of the nearest-neighbour hopping proportional to\({1 \mathord{\left/ {\vphantom {1 {\sqrt d }}} \right. \kern-\nulldelimiterspace} {\sqrt d }}\) and of the nearest-neighbour interaction proportional to 1/d. Due to this scaling the Hartree approximation becomes exact in infinite dimensions. We show that 1/d corrections comprise the Fock diagram and the local correlation diagram in the self-consistent Dyson equation. This approach is applied to simple-cubic systems in dimensiond=1, 2 and 3. Ground state properties and the charge-density wave phase diagram are calculated. AtT=0 the inclusion of 1/d terms gives only small corrections to the leading Hartree contribution ind=2, 3. ForT>0, however, the 1/d corrections are important. They lead to a non-negligible reduction of the critical temperature. Ind=1 the 1/d corrections are very large, but they do not succeed in removing the spurious phase transition atT>0. The 1/d approach provides a good and tractable approximation ind=3 and probably ind=2, which allows also further systematic improvement.