HIDDEN Z(2)XZ(2) SYMMETRY IN QUANTUM SPIN CHAINS WITH ARBITRARY INTEGER SPIN

We study integer S > 1 spin chains. We extend the Kennedy-Tasaki non-local unitary transformation for S = 1 to arbitrary integer S. We show the main results of Kennedy and Tasaki are maintained for S > 1: Heisenberg-type Hamiltonians are transformed to Hamiltonians of nearest-neighbour interactions with Z2 x Z2 symmetry, and the den Nijs-Rommelse string observables are transformed to the ferromagnetic correlation observables. We assert that in general values of integer S there exist several phases with the hidden Z2 x Z2 symmetry breaking. The den Nijs-Rommelse string order parameters, which measure the hidden Z2 x Z2 symmetry breaking, are calculated explicitly for several variants of the VBS-type states. In the standard VBS state, the hidden Z2 x Z2 symmetry breaks down when S is odd but remains unbroken when S is even. Our results for partially dimerized VBS states suggest that the hidden Z2 x Z2 symmetry breaking can be used to detect the successive dimerization transitions predicted by Affleck and Haldane. Some new anisotropic VBS-type states are investigated. The result suggests that there are successive phase transitions when we increase the uniaxial anisotropy in a Heisenberg-type model. Other new VBS-type states with long-range order are considered, and their relevance to the phase diagram of the Heisenberg X X Z model and the magnetization process of antiferromagnets is investigated. We introduce an extended string order parameter which possesses a characteristic behaviour in the partially dimerized VBS states.