Next nearest neighbour interactions in the Heisenberg model

Abstract

The Bethe ansatz is used to analytically solve the Heisenberg model with nearest neighbour interactions for spin-1/2 particles in an one dimensional chain. Our goal is to find out if the Bethe ansatz can be extended to nearest and next nearest neighbour interactions and to gain insight into the system with exact diagonalization. We find that this cannot be done. Because of certain assumptions made in the Bethe ansatz, the method fails for next nearest neighbour interactions.