Singular Solutions to the Bethe Ansatz Equations and Rigged Configurations

Understand

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.