Exact Solution for Two $δ$-Interacting Bosons on a Ring in the Presence of a $δ$-Barrier: Asymmetric Bethe Ansatz for Spatially Odd States

• URL: http://arxiv.org/abs/2508.17371v4
• Date: Sat, 25 Oct 2025 15:45:10 GMT
• Title: Exact Solution for Two $δ$-Interacting Bosons on a Ring in the Presence of a $δ$-Barrier: Asymmetric Bethe Ansatz for Spatially Odd States
• Authors: Maxim Olshanii, Mathias Albert, Gianni Aupetit-Diallo, Patrizia Vignolo, Steven G. Jackson,
• Abstract summary: We study the problem of two one-dimensional, short-range-interacting bosons on a ring in the presence of a $delta$-function barrier.<n>We find that when the barrier is converted to a $delta$-well with strength equal to that of the particle-particle interaction, the system exhibits the spectrum of its non-interacting counterpart.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 $\delta$-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 [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 $\delta$-barrier is converted to a $\delta$-well with strength equal to that of the particle-particle interaction, the system exhibits the spectrum of its non-interacting 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.

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