Solitons in the anisotropic xy chain: semiclassical treatment of quantum effects

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Abstract
The authors have investigated soliton solutions and their contribution to the specific heat for the anisotropic xy chain in the classical and semiclassical approximation. The soliton solutions, which can be given analytically for the discrete classical chain, are shown to be stable. In the continuum approximation the classical system is equivalent to the sine-Gordon model. The energy of the moving soliton is determined up to second order in the soliton velocity. In the semiclassical approximation the magnetic chain with spin S is equivalent to a quantum sine-Gordon chain with coupling constant g2=(32/S(S+1))12/. Using the magnon phase shift in the presence of a dilute gas of solitons the authors have calculated the specific heat. They find that the semiclassical approximation reasonably describes the transition from the classical limit to the S=1/2 model as solved exactly by Lieb. Schultz and Mattis (1961).