Singular Solutions to the Bethe Ansatz Equations and Rigged Configurations

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.

24 pages, final version, elucidated the relationship between the rigged configurations and string solutions (Section 3.1)

References in corpus (4)

• Crystal interpretation of Kerov-Kirillov-Reshetikhin bijection
• Tau functions in combinatorial Bethe ansatz
• Bethe ansatz and inverse scattering transform in a periodic box-ball system
• The Bethe ansatz in a periodic box-ball system and the ultradiscrete Riemann theta function

Cited by in corpus (5)

• Twisting singular solutions of Bethe's equations
• Non Self-conjugate Strings, Singular Strings and Rigged Configurations in the Heisenberg Model
• Singular eigenstates in the even(odd) length Heisenberg spin chain
• Heisenberg model and Rigged Configurations
• Rigged Configurations Approach For The Spin-1/2 Isotropic Heisenberg Model