Semiclassical description of spin ladders

Abstract

The Heisenberg spin ladder is studied in the semiclassical limit, via a mapping to the nonlinear $\sigma$ model. Different treatments are needed if the inter-chain coupling $K$ is small, intermediate or large. For intermediate coupling a single nonlinear $\sigma$ model is used for the ladder. Its predicts a spin gap for all nonzero values of $K$ if the sum $s+\tilde{s}$ of the spins of the two chains is an integer, and no gap otherwise. For small $K$, a better treatment proceeds by coupling two nonlinear sigma models, one for each chain. For integer $s=\tilde{s}$, the saddle-point approximation predicts a sharp drop in the gap as $K$ increases from zero. A Monte-Carlo simulation of a spin 1 ladder is presented which supports the analytical results.

8 pages, RevTeX 3.0, 4 PostScript figures

References in corpus (3)

• Equivalence of the antiferromagnetic Heisenberg ladder to a single $S=1$ chain
• Calculation of the singlet-triplet gap of the antiferromagnetic Heisenberg Model on the ladder
• Haldane gap in the quasi one-dimensional nonlinear $\sigma$-model

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