Semiclassical description of spin ladders

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+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 {σ} models, one for each chain. For integer s=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.