Stability of Insulating Phases in the Hubbard Model: a Cluster Expansion

Abstract

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 $\bar{t}<U/4d$. This implies an upper bound for the decay length of the Green's function.

18 pages, Plain-TeX, TKM 08/93