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Generalized local interactions in 1D: solutions of quantum many-body systems describing distinguishable particles

Martin Hallnäs·Edwin Langmann·Cornelius Paufler
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Abstract

As is well-known, there exists a four parameter family of local interactions in 1D. We interpret these parameters as coupling constants of delta-type interactions which include different kinds of momentum dependent terms, and we determine all cases leading to many-body systems of distinguishable particles which are exactly solvable by the coordinate Bethe Ansatz. We find two such families of systems, one with two independent coupling constants deforming the well-known delta interaction model to non-identical particles, and the other with a particular one-parameter combination of the delta- and (so-called) delta-prime interaction. We also find that the model of non-identical particles gives rise to a somewhat unusual solution of the Yang-Baxter relations. For the other model we write down explicit formulas for all eigenfunctions.

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Martin Hallnäs, Edwin Langmann, Cornelius Paufler. 2004-09-06. Generalized local interactions in 1D: solutions of quantum many-body systems describing distinguishable particles. https://doi.org/10.1088/0305-4470/38/22/018

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