Haldane gap in a S=1 exchange model with long-range interactions

Abstract

The ground-state properties of the S=1 Haldane-Shastry model are studied using a modified Lanczos algorithm and diagonalizing exactly small chains. We find evidence that, as for the antiferromagnetic Heisenberg model, the spectrum shows a gap, in contrast to the S=1/2 case. The correlation functions <S^{z}(0)S^{z}(m)> decay exponentially for large m. We find that the correlation functions for the Haldane-Shastry model decay faster than for the Heisenberg model. We estimate the infinite system limit for the ground-state energy, value of the gap and correlation functions.