Large-N behaviour of string solutions in the Heisenberg model

We investigate the large-N behaviour of the complex solutions for the two-magnon system in the S = 1/2 Heisenberg XXZ model. The Bethe ansatz equations are numerically solved for the string solutions with a new iteration method. Clear evidence of the violation of the string configurations is found at N = 22, 62, 121, 200, 299, 417, but the broken states are still Bethe states. The number of Bethe states is consistent with the exact diagonalization, except for one singular state.