Twisting singular solutions of Bethe's equations

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.Comment: 10 pages; v2: references added; v3: introduction expanded, and more references adde