Anatol N. Kirillov, Reiho Sakamoto
Published 2014-02-04, updated 2014-03-25Version 2
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.
Comments: 24 pages, final version, elucidated the relationship between the rigged configurations and string solutions (Section 3.1)
Journal: J. Phys. A: Math. Theor. 47 (2014) 205207 (20pp)
Rigged Configurations Approach For The Spin-1/2 Isotropic Heisenberg Model
Bethe's Quantum Numbers And Rigged Configurations
Incarnations of XXX $\widehat{\frak{sl}_N}$ Bethe ansatz equations and integrable hierarchies
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