Haldane gap in three dimensions: A rigorous example

Abstract

A quasi-one-dimensional S=1 antiferromagnet with XXZ-type intrachain couplings and Ising-type interchain couplings is studied. It has been suggested that when the interchain couplings are sufficiently small such a system has no long-range order, even at T=0, because of strong quantum fluctuation caused by the Haldane gap. Treating the problem in a restricted Hilbert space which describes the low-energy behavior of S=1 antiferromagnets rather accurately, we prove two theorems which establish the existence of a unique disordered ground state with a gap.