A Comparison of the Bethe Ansatz and Green Function Approaches to Two-Magnon States of the Ferromagnetic Chain

Abstract

Until recently investigations of magnetic excitations in the generalized Heisenberg chain by the Bethe Ansatz method [1] were largely limited to S=½. The exception being for special models with particular coefficients, e.g. the completely integrable “Russian” models [2], which have recently been studied by TAKHTAJAN [3] and BABUJIAN [4] for general S, and PARKINSON and BONNER for S=1 [5]. The lack of complete integrability in the general case means that the Bethe Ansatz fails in general for n-magnon excitations. However MATTIS [6] has shown that the Bethe Ansatz could be used for two magnon excitations (n=2) from the ferromagnetic ground state for S>½. Two groups have recently given a fuller analysis of two-magnon states. The possibility of higher spin opens the way for inclusion of uniaxial anisotropy and higher order exchange.KeywordsGreen FunctionUniaxial AnisotropyMagnetic ExcitationNext Near NeighbourGreen Function MethodThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.