MEAN-FIELD APPROACH TO ANTIFERROMAGNETIC DOMAINS IN THE DOPED HUBBARD-MODEL

We present a restricted path integral approach to the two-dimensional and three-dimensional repulsive Hubbard model. In this approach the pa rtition function is approximated by restricting the summation over all states to a (small) subclass that is chosen so as to well represent t he important states. This procedure generalizes mean-field theory and can be systematically improved by including more states or fluctuation s. We analyze in detail the simplest of these approximations, which co rresponds to summing over states with local antiferromagnetic (AF) ord er. If in the states considered the AF order changes sufficiently litt le in space and time, the path integral becomes a finite-dimensional i ntegral for which the saddle point evaluation is exact. This leads to generalized mean-field equations allowing for the possibility of more than one relevant saddle point. In a big parameter regime (both in tem perature and filling), we find that this integral has two relevant sad dle points, one corresponding to finite AF order and the other without . These degenerate saddle points describe a phase of AF ordered fermio ns coexisting with free, metallic fermions. We argue that this mixed p hase is a simple mean-field description of a variety of possible inhom ogeneous states, appropriate on length scales where these states appea r homogeneous. We sketch systematic refinements of this approximation, which can give more detailed descriptions of the system.