Antiferromagnetic spin-waves in the repulsive Hubbard model — a new functional integral formalism

Abstract

We develop a new functional integral approach to the Hubbard model, which at the saddle point respects rotational invariance and does not a priori assume long-range order (LRO). Using this approach, we study collective spin fluctuations in the repulsive half filled Hubbard model on a square lattice. Our result differs from recent calculations employing the random phase approximation (RPA) in the appearance of an important wave function renormalization factor 0 ≤ R z ≤ 1. The RPA results can be reproduced in a very simple way provided one sets R z = 1 for all U/ t. However, R z becomes very small weak coupling, implying that collective spin-wave modes destroy the LRO for sufficiently small U/ t even at zero temperature. We suggest the possibility that at weak coupling the half filled Hubbard model on a square lattice is an antiferromagnetic insulator without LRO.