HALLNÄS, M. and LANGMANN, E., 2005. Exact solutions of two complementary one-dimensional quantum many-body systems on the half-line. Journal of Mathematical Physics, 46 (5), http://dx.doi.org/10.1063/1.1865320, 15pp.
We consider two particular one-dimensional quantum many-body systems with local interactions related to the root system CN. Both models describe identical particles moving on the half-line with nontrivial boundary conditions at the origin, but in the first model the particles interact with the delta interaction while in the second via a particular momentum dependent interaction commonly known as delta-prime interaction. We show that the Bethe ansatz solution of the delta-interaction model is consistent even for the general case where the particles are distinguishable, whereas for the delta-prime interaction it only is consistent and nontrivial in the fermion case. We also establish a duality between the bosonic delta- and the fermionic delta-prime model, and we elaborate on the physical interpretations of these models.