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

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

1995-02-07

arxiv.org/abs/hep-th/9502041v1

Nucl.Phys. B446 (1995) 461-484

Physics

High Energy Physics

High Energy Physics - Theory

25 pages, LaTeX

Scientific paper

10.1016/0550-3213(95)00168-R

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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