A Weak Coupling Expansion for the Hubbard Model on a 4×4 Cluster

Dai S. Hirashima

Barry Friedman

I present a scheme for performing weak-coupling expansions for the Hubbard model on square clusters near half-filling. Using this scheme the 6 × 6 cluster with 2, 3 and 4 holes is considered. I have calculated the ground-state quantum numbers for the 3- and 4-hole cases. In the 3-hole case I find a nonzero momentum near the (±π/2, ±π/2) points, while for the four-hole case the momentum is (0, 0). The calculation of low-lying excited states indicates the opening of a spin gap as one dopes away from half-filling.

S. Pairault, David Sénéchal, A.–M. S. Tremblay

青木 秀夫, 浩一 草部

energy calculated via weak coupling perturbation theory captures reasonably well the binding energy at intermediate coupling.A possible extension of the weak coupling expansion to larger clusters is discussed.Dispersion of Low-lying Excitaions in Half-fi I led and Doped 10 Hubbard Model

H. Schweitzer, G. Czycholl

K. Ziegler

The stability of the insulating regime of the Hubbard model on a $d$-dimensional lattice, which is characterized by an exponential decay of the Green's functions, is investigated in terms of a cluster expansion. This expansion for the Green's function is organized in terms of connected clustered transfer matrices. An upper bound for the expansion terms is derived for the hopping rate ${\bar t}$ depending on the coupling constant $U$ as ${\bar t}