On certain classes of exact solutions of two magnon states in the Heisenberg spin chain

This paper explores some modifications in the Bethe ansatz which gives the analytical solution of the one-dimensional Heisenberg spin chain model. We propose a master equation for lattice momenta calculation of the two magnon state and show both analytically and numerically that using this condition how one can easily derive the lattice momenta which are real. Thereafter, we derive a total of four different cases for the class $$C_3$$ solution (complex lattice momenta) of the two magnon state based on even or odd total number and half the number of spins. As an example, we show the eigenvalue spectrum of the one magnon and the two magnon state for the 32-spin system. After that, we modify the Bethe ansatz relation for more than two spins in neighboring site spin flip group for the r magnon state