Dimensional Crossover in Quantum Antiferromagnets

TL;DR

This paper analyzes how quantum antiferromagnets transition from two-dimensional to one-dimensional behavior as the width of the system varies, providing explicit formulas and exploring conformal field theory aspects.

Contribution

It offers analytical expressions for correlation length and spin gap during the dimensional crossover in spin-$S$ Heisenberg antiferromagnets, including the effects of spin type and system width.

Findings

Explicit formulas for correlation length and spin gap for various spins and widths.

Demonstration of the suppression of $c=1$ conformal behavior in certain limits.

Relevance of results to spin-ladder systems with $S=1/2$.

Abstract

The dimensional crossover in a spin-$S$ nearest neighbor Heisenberg antiferromagnet is discussed as it is tuned from a two-dimensional square lattice, of lattice spacing $a$, towards a spin chain by varying the width $L_y$ of a semi-infinite strip $L_x\times L_y$. For integer spins and arbitrary $L_y$, and for half integer spins with $L_y/a$ an arbitrary even integer, explicit analytical expressions for the zero temperature correlation length and the spin gap are given. For half integer spins and $L_y/a$ an odd inetger, it is shown that the $c=1$ behavior of the $SU(2)_1$ WZW fixed point is squeezed out as the width $L_y\to \infty$; here $c$ is the conformal charge. The results specialized to $S=1/2$ are relevant to spin-ladder systems.