The Bethe Ansatz

We simply have \(M = N/2-2 = M_1^<\) finite rapidity one-strings. We have \(I^{1,\infty} = \frac{N}{4} + \frac{3}{2}\) and \(I^{\mbox{max}} = \frac{N}{4} + \frac{1}{2}\). The number of states is thus \(\left( \begin{array}{c} N/2 + 2 \\ N/2 - 2 \end{array} \right) = \frac{(N+4) (N+2) N(N-2)}{384}\). These are the \(S = 2\), \(S^z = 2\) four-spinon states.