Gapless spectrum in a class of S=1 exchange models with long-range interactions

TL;DR

This paper demonstrates that a class of long-range S=1 antiferromagnetic exchange models lack a Haldane gap, showing power-law decay of correlations and potential relevance to impurity spin systems with RKKY interactions.

Contribution

It introduces a new class of integer spin chains with long-range interactions that do not exhibit a Haldane gap, contrasting with known models.

Findings

Correlation functions decay as a power law

Models lack a Haldane gap

Relevance to impurity spins with RKKY interactions

Abstract

We present evidence for the absence of a gap in a class of S=1 antiferromagnetic exchange models. The spin exchange is long-ranged of the type $-(-1)^{i-j}/|i-j|^{\alpha}$ where $1<\alpha<3$. We have shown previously that without the alternating factor the model for $\alpha=2$ (S=1 Haldane-Shastry model) has a gap, exponentially decaying correlation functions and exponentially small susceptibility at very low temperatures. In the case of the alternated interaction the stabilizing next nearest neighbor ferromagnetic interaction changes qualitatively the behavior of the system. We have studied the groundstate and first excited state using a modified Lanczos algorithm for system sizes up to 16 sites. Also, we performed exact diagonalization for systems up to 8 sites and obtained the thermodynamics. The correlation functions decay with distance like a power law. These models define a new class of integer spin chains that do not show a Haldane gap. The results may be relevant to describe impurity spins coupled by a RKKY-interaction through a half-filled conduction-electron band.