Exact solution for the spin s Xxz quantum chain with non diagonal twists

Mathematics Research Report MRR95-014

Exact solution for the spin-s XXZ quantum chain with non diagonal twists

C.M. Yung and M.T. Batchelor

Abstract: We study integrable vertex models and quantum spin chains with toroidal boundary conditions. An interesting class of such boundaries is associated with non-diagonal twist matrices. For such models there are no trivial reference states upon which a Bethe ansatz calculation can be constructed, in contrast to the well-known case of periodic boundary conditions. In this paper we show how the transfer matrix eigenvalue expression for the spin-s XXZ chain twisted by the charge-conjugation matrix can in fact be obtained. The technique used is the generalization to spin-s of the functional relation method based on ``pair-propagation through a vertex". The Bethe ansatz-type equations obtained reduce, in the case of lattice size N=1, to those recently found for the Hofstadter problem of Bloch electrons on a square lattice in a magnetic field.

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