Semiclassical description of spin ladders

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Abstract
The Heisenberg spin ladder is studied in the semiclassical limit, via a mapping to the nonlinear σ model. Different treatments are needed if the interchain coupling K is small, intermediate, or large. For intermediate coupling a single nonlinear σ model is used for the ladder. It predicts a spin gap for all nonzero values of K if the sum s+s̃ 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 σ models, one for each chain. For integer s=s̃, 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.
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