SYSTEMATIC STUDY ON ANTIFERROMAGNETIC STATES OF THE HUBBARD-MODEL WITH THE DIMENSION D=1,2,3 AND INFINITY

Antiferromagnetic states of the half-filled Hubbard model on the d=1,2,3, and dimensional lattices are systematically studied by using the Gutzwiller-type analytical approximation based on the slave-boson functional-integral approach. In all the cases investigated, antiferromagnetic states have lower energies than paramagnetic states even for infinitesimally small interactions, U. Calculated results of the ground-state energy E and the sublattice moment m for d=2 and 3 are in very good agreement with those of the Monte Carlo simulations. Even for d=1 the antiferromagnetic state in our Gutzwiller-type approximation has energy much closer to the exact one than the paramagnetic states in Gutzwillers approximation and in Metzner-Vollhardts approximation-free method. On the basis of the 1/d plot of E and m, a possibility of the 1/d expansion starting from the limit of d= is discussed. It is also shown that the Brinkman-Rice metal-insulator transition does not take place at finite U for all d. © 1990 The American Physical Society.