THE STRUCTURE OF BETHE ANSATZ SOLUTIONS FOR THE CHAIN N=8, r=4

Abstract

The Bethe Ansatz can be treated using two approaches: The Co-ordinate Bethe Ansatz (CBA) and The Algebraic Bethe Ansatz (ABA). In this paper the relation between the solutions given by these two methods is addressed. The considerations are based on the finite Heisenberg magnet with N=8 nodes and for r=4 reversed spins s=1/2. Both methods provide consistent solutions in the entire Brillouin zone (BZ). Moreover there is a special point — a border of the BZ — for both approaches, in which the solutions are not well-defined.