Weakly Coupled Antiferromagnetic Quantum Spin Chains

TL;DR

This paper investigates how weak interchain couplings induce magnetic long-range order in quasi-one-dimensional antiferromagnets, revealing critical behaviors and phase transitions using a combination of exact and renormalization group methods.

Contribution

It provides a detailed analysis of the onset of magnetic order in weakly coupled spin chains, including effects of bond alternation and relevance to other quantum systems.

Findings

Long-range order develops at zero temperature with infinitesimal interchain coupling.

Order-disorder transition occurs at finite coupling with bond alternation.

Relevance to doped quantum antiferromagnets and quantum Hall multilayers.

Abstract

Quasi-one-dimensional quantum antiferromagnets formed by a d-dimensional hypercubic lattice of weakly coupled spin-1/2 antiferromagnetic Heisenberg chains are studied by combining exact results in one-dimension and renormalization group analyses of the interchain correlations. It is shown that d-dimensional magnetic long-range order develops at zero-temperature for infinitesimal antiferromagnetic or ferromagnetic interchain couplings. In the presence of weak bond alternations, the order-disorder transition occurs at a finite interchain coupling. Relevances to the lightly doped quantum antiferromagnets and multi-layer quantum Hall systems are discussed.