Origin of the singular Bethe ansatz solutions for the Heisenberg XXZ spin chain

We investigate symmetry properties of the Bethe ansatz wave functions for t he Heisenberg XXZ spin chain. The XXZ Hamiltonian commutes simultaneously w ith the shift operator T and the lattice inversion operator V in the space of Ohm = +/-1 with Ohm the eigenvalue of T. We show that the Bethe ansatz s olutions with normalizable wave functions cannot be the eigenstates of T an d V with quantum number (Ohm, Y) = (+/-1, =1) where Y is the eigenvalue of V. Therefore, the Bethe ansatz wave functions should be singular for nondeg enerate eigenstates of the Hamiltonian with quantum number (Ohm, Y) = (+/-1 , =1). It is also shown that such states exist in any nontrivial down-spin number sector and that the number of them diverges exponentially with the c hain length. (C) 2000 Published by Elsevier Science B.V. All rights reserve d.