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

19 pages, 13 figures, RevTex, improved version, to appear in Journal of Physics: Condensed Matter

References in corpus (5)

• Magnetization plateaus in spin chains: ``Haldane gap'' for half-integer spins
• Equivalence of the antiferromagnetic Heisenberg ladder to a single $S=1$ chain
• RKKY interaction and Kondo screening cloud for correlated electrons
• Phase diagram and hidden order for generalized spin ladders
• Haldane gap in a S=1 exchange model with long-range interactions

Cited by in corpus (4)

• Kaleidoscope of quantum phases in a long-range interacting spin-1 chain
• Spin Waves in Antiferromagnetic Spin Chains with Long Range Interactions
• Gifts from long-range interaction: Emergent gapless topological behaviors in quantum spin chain
• On the ground-state properties of antiferromagnetic half-integer spin chains with long-range interactions