Solving the open XXZ spin chain with nondiagonal boundary terms at roots of unity

Abstract

We consider the open XXZ quantum spin chain with nondiagonal boundary terms. For bulk anisotropy value \eta = i \pi/(p+1), p= 1, 2, ..., we propose an exact (p+1)-order functional relation for the transfer matrix, which implies Bethe-Ansatz-like equations for the corresponding eigenvalues. The key observation is that the fused spin-(p+1)/2 transfer matrix can be expressed in terms of a lower-spin transfer matrix, resulting in the truncation of the fusion hierarchy.