Abstract
For a one-dimensional chain with exponential plus linear interactions the asymptotic wave functions are constructed by Bethe's ansatz using the exact two-body phase shift. Ground state energy and excitations are obtained by Lieb's method for two different boundary conditions. In the strongly anharmonic (weak coupling) regime the system behaves effectively like a gas of hard spheres with constant attraction, where the radius of the spheres is the scattering length. In the classical (strong coupling) limit the particle and hole excitations of the quantum problem reduce to solitons and phonons, respectively (this is Sutherland's result for the classical and low density limit of a model with sinh−2 r interactions). Finally the type of statistics relevant for the excitations is discussed for both regimes.
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Mertens, F.G. Bethe ansatz for the Toda lattice: Ground state and excitations. Z. Physik B - Condensed Matter 55, 353–360 (1984). https://doi.org/10.1007/BF01304087
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DOI: https://doi.org/10.1007/BF01304087