TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhysCore.8.4.083
TI  - Exact solution for two $\delta$-interacting bosons on a ring in the presence of a $\delta$-barrier: Asymmetric Bethe Ansatz for spatially odd states
PY  - 2025/11/12
UR  - https://www.scipost.org/SciPostPhysCore.8.4.083
JF  - SciPost Physics Core
JA  - SciPost Phys. Core
VL  - 8
IS  - 4
SP  - 083
A1  - Olshanii, Maxim
AU  - Albert, Mathias
AU  - Aupetit-Diallo, Gianni
AU  - Vignolo, Patrizia
AU  - Jackson, Steven G.
AB  - 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 [D. Sen, Int. J. Mod. Phys. A 14, 1789 (1999); A. G. Volosniev et al., Nat. Commun. 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.
ER  -

@Article{10.21468/SciPostPhysCore.8.4.083,
	title={{Exact solution for two $\delta$-interacting bosons on a ring in the presence of a $\delta$-barrier: Asymmetric Bethe Ansatz for spatially odd states}},
	author={Maxim Olshanii and Mathias Albert and Gianni Aupetit-Diallo and Patrizia Vignolo and Steven G. Jackson},
	journal={SciPost Phys. Core},
	volume={8},
	pages={083},
	year={2025},
	publisher={SciPost},
	doi={10.21468/SciPostPhysCore.8.4.083},
	url={https://scipost.org/10.21468/SciPostPhysCore.8.4.083},
}