q-DEFORMATIONS OF QUANTUM SPIN CHAINS WITH EXACT VALENCE–BOND GROUND STATES

Bruno Nachtergaele

Bruno Nachtergaele

M. Fannes, Bruno Nachtergaele, Reinhard F. Werner

Murray T. Batchelor, C M Yung

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 neighboring 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-½ Majumdar-Ghosh model.

Charlotte Gils, Eddy Ardonne, Simon Trebst +3 more

Paul Louis Iske, W.J. Caspers

The ground state(s) of a Hamiltonian, introduced by Affleck, Kennedy, Lieb and Tasaki, in connection with the Valence-Bond-Solid (VBS) states, are explicitly given for the spin-1 chains. The structure of these ground states is a rather simple one. For a closed chain we find a unique ground state; for the open chain we find a fourfold-degenerate ground state. The ground state correlation function for the ring is calculated.