On the Bethe Hypothesis for the Anisotropic Heisenberg Chain

The two-reversed-spin problem for the anisotropic Heisenberg linear chain is solved in a straightforward and rigorous way. The method involves the solution of a second-order partial difference equation and does not necessitate the use of the Bethe hypothesis. It is shown that, although most of the eigenfunctions are of the Bethe form, there exist special states which, a priori, cannot be so written. In addition, a simple method is presented for enumerating the bound states. Detailed connections between the present solution and that given by Bethe, and later by Orbach, are discussed.