Bounds for correlation functions of the Heisenberg antiferromagnet

Abstract

We present rigorous lower bounds for spin correlations of the quantum Heisenberg antiferromagnet under the assumption of long range order, at zero as well as nonzero temperatures in the form of a crossover function. These are obtained by combining a recent inequality giving lower bounds to correlation functions with infrared upper bounds for the static susceptibility. The functional forms of the lower bounds are identical with upper (infrared) bounds for the correlation functions implying that the nature of divergence of the correlations near the antiferromagnetic zone boundary is determined. The form agrees with the prediction of the theory of spin waves. They also present a generalized inequality in quantum statistical mechanics that contains the previously known cases as special cases.