q-deformations of quantum spin chains with exact valence-bond ground states

Abstract

Quantum spin chains with exact valence-bond ground states are of great interest in condensed-matter physics. A class of such models was proposed by Affleck et al., each of which is su(2)-invariant and constructed as a sum of projectors onto definite total spin states at neighbouring sites. We propose to use the machinery of the q-deformation of su(2) to obtain generalisations of such models, and work out explicitly the two simplest examples. In one case we recover the known anisotropic spin-1 VBS model while in the other we obtain a new anisotropic generalisation of the spin-1/2 Majumdar-Ghosh model.

9 pages, LaTeX, MRR-011-94 This paper has been expanded to include a discussion of the ground state correlations and the gap to excitations in the q-deformed generalisation of the Majumdar-Ghosh model

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