Integrability and weak diffraction in a two-particle Bose–Hubbard model
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Publication:2936422
DOI10.1088/1751-8113/47/46/465303zbMATH Open1301.82017arXiv1403.6875OpenAlexW2056600491MaRDI QIDQ2936422
Author name not available (Why is that?)
Publication date: 16 December 2014
Published in: (Search for Journal in Brave)
Abstract: A recently introduced one-dimensional two-particle Bose-Hubbard model with a single impurity is studied on finite lattices. The model possesses a discrete reflection symmetry and we demonstrate that all eigenstates odd under this symmetry can be obtained with a generalized Bethe ansatz if periodic boundary conditions are imposed. Furthermore, we provide numerical evidence that this holds true for open boundary conditions as well. The model exhibits backscattering at the impurity site -- which usually destroys integrability -- yet there exists an integrable subspace. We investigate the non-integrable even sector numerically and find a class of states which have almost the Bethe ansatz form. These weakly diffractive states correspond to a weak violation of the non-local Yang-Baxter relation which is satisfied in the odd sector. We bring up a method based on the Prony algorithm to check whether a numerically obtained wave function is in the Bethe form or not, and if so, to extract parameters from it. This technique is applicable to a wide variety of other lattice models.
Full work available at URL: https://arxiv.org/abs/1403.6875
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