Twisting singular solutions of Bethe's equations

TL;DR

This paper investigates singular solutions of Bethe's equations in spin chains, using twist regularization to identify which solutions correspond to valid eigenstates of the system.

Contribution

It introduces a twist regularization method to determine the physicality of singular solutions in Bethe's equations for XXX and XXZ spin chains.

Findings

Derived conditions for singular solutions to be physical.

Established criteria for eigenvalues and eigenvectors validity.

Enhanced understanding of solution regularization in integrable models.

Abstract

The Bethe equations for the periodic XXX and XXZ spin chains admit singular solutions, for which the corresponding eigenvalues and eigenvectors are ill-defined. We use a twist regularization to derive conditions for such singular solutions to be physical, in which case they correspond to genuine eigenvalues and eigenvectors of the Hamiltonian.