Internal parity symmetry and degeneracy of Bethe Ansatz strings in the isotropic heptagonal magnetic ring

The exact Bethe eigenfunctions for the heptagonal ring within the isotropic XXX model exhibit a doubly degenerated energy level in the three-deviation sector at the centre of the Brillouin zone. We demonstrate an explicit construction of these eigenfunctions by use of algebraic Bethe Ansatz, and point out a relation of degeneracy to parity conservation, applied to the configuration of strings for these eigenfunctions. Namely, the internal structure of the eigenfunctions (the 2-string and the 1-string, with opposite quasimomenta) admits generation of two mutually orthogonal eigenfunctions clue to the fact that the strings which differ by their length are distinguishable objects. (C) 2013 Elsevier B.V. All rights reserved.