Exact solution for two δ-interacting bosons on a ring in the presence of a δ-barrier: Asymmetric Bethe Ansatz for spatially odd states

In this article, we apply the recently proposed Asymmetric Bethe Ansatz method to the problem of two one-dimensional, short-range-interacting bosons on a ring in the presence of a δ-function barrier. Only half of the Hilbert space-namely, the two-body states that are odd under point inversion about the position of the barrier-is accessible to this method. The other half is presumably non-integrable. We consider benchmarking the recently proposed 1/g expansion about the hard-core boson point [D. Sen, Int. J. Mod. Phys. A 14, 1789 (1999); A. G. Volosniev, D. V. Fedorov, A. S. Jensen, M. Valiente, N. T. Zinner, Nature Communications 5, 5300 (2014)] as one application of our results. Additionally, we find that when the δ-barrier is converted to a δ-well with strength equal to that of the particle-particle interaction, the system exhibits the spectrum of its noninteracting counterpart while its eigenstates display features of a strongly interacting system. We discuss this phenomenon in the “Summary and Future Research” section of our paper.