Scaling Theory of Antiferromagnetic Heisenberg Ladder Models

TL;DR

This paper develops a scaling theory for antiferromagnetic Heisenberg ladder models, revealing distinct behaviors for even and odd leg ladders, including energy gap scaling and critical phases.

Contribution

It provides a comprehensive finite-size scaling analysis distinguishing even and odd leg ladders in the antiferromagnetic Heisenberg model, highlighting their critical and gapped phases.

Findings

Energy gap scales as ΔE ∼ J_⊥ for even-leg ladders.

Odd-leg ladders exhibit a critical phase with central charge c=1.

Criticality persists for all J_⊥ > 0 in odd-leg ladders.

Abstract

The $S=1/2$ antiferromagnetic Heisenberg model on multi-leg ladders is investigated. Criticality of the ground-state transition is explored by means of finite-size scaling. The ladders with an even number of legs and those with an odd number of legs are distinguished clearly. In the former, the energy gap opens up as $\Delta E\sim{J_\perp}$, where ${J_\perp}$ is the strength of the antiferromagnetic inter-chain coupling. In the latter, the critical phase with the central charge $c=1$ extends over the whole region of ${J_\perp}>0$.