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A Note on Dressed S-Matrices in Models with Long-Range Interactions

Fabian H. L. Essler
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Abstract

The {\sl dressed} Scattering matrix describing scattering of quasiparticles in various models with long-range interactions is evaluated by means of Korepin's method\upref vek1/. For models with ${1\over\sin^2(r)}$-interactions the S-matrix is found to be a momentum-independent phase, which clearly demonstrates the ideal gas character of the quasiparticles in such models. We then determine S-matrices for some models with ${1\over\sinh^2(r)}$-interaction and find them to be in general nontrivial. For the ${1\over r^2}$-limit of the ${1\over\sinh^2(r)}$-interaction we recover trivial S-matrices, thus exhibiting a crossover from interacting to noninteracting quasiparticles. The relation of the S-matrix to fractional statistics is discussed.

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Fabian H. L. Essler. 1994-12-19. A Note on Dressed S-Matrices in Models with Long-Range Interactions. https://doi.org/10.1103/physrevb.51.13357

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