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

TL;DR

This paper investigates the ground-state properties of the S=1 Haldane-Shastry model with long-range interactions, revealing a spectral gap and exponential decay of correlations, similar to the antiferromagnetic Heisenberg model.

Contribution

It provides the first detailed analysis of the S=1 Haldane-Shastry model, demonstrating the presence of a gap and characterizing correlation decay using exact diagonalization methods.

Findings

Spectral gap confirmed in the S=1 Haldane-Shastry model.

Correlation functions decay exponentially and faster than in the S=1/2 case.

Estimated ground-state energy, gap, and correlation functions for infinite systems.

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.