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Singular Solutions to the Bethe Ansatz Equations and Rigged Configurations

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arxiv 1402.0651 v2 pith:F6J4K2X5 submitted 2014-02-04 math-ph math.MP

Anatol N. Kirillov , Reiho Sakamoto This is my paper
classification math-phmath.MP
keywords betheansatzequationssolutionsconfigurationsconjecturenumberrigged
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abstract

We provide a conjecture for the following two quantities related with the spin-$\frac{1}{2}$ isotropic Heisenberg model defined over rings of even lengths: (i) the number of the solutions to the Bethe ansatz equations which correspond to non-zero Bethe vectors; (ii) the number of physical singular solutions of the Bethe ansatz equations in the sense of Nepomechie-Wang. The conjecture is based on a natural relationship between the solutions to the Bethe ansatz equations and the rigged configurations.

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Cited by 1 Pith paper

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  1. Integrable 3-Site, Tilted, Extended Bose-Hubbard Model with Nearest-Neighbour Interactions

    cond-mat.quant-gas 2025-06 conditional novelty 6.0 of 10

    A carefully tuned three-site extended Bose-Hubbard model with nearest-neighbour interactions is integrable and solved exactly by a Bethe ansatz.

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