Hidden Z2*Z2 symmetry in quantum spin chains with arbitrary integer spin

Abstract

The author studies integer S>1 spin chains. He extends the Kennedy-Tasaki nonlocal unitary transformation for S=1 to arbitrary integer S. He shows the main results of Kennedy and Tasaki (1992) are maintained for S>1: Heisenberg-type Hamiltonians are transformed to Hamiltonians of nearest-neighbour interactions with Z2*Z2 symmetry, and the den Nijs-Rommelse string observables are transformed to the ferromagnetic correlation observables. He asserts that in general values of integer S there exist several phases with the hidden Z2*Z2 symmetry breaking. The den Nijs-Rommelse string order parameters, which measure the hidden Z2*Z2 symmetry breaking, are calculated explicitly for several variants of the VBS-type states. In the standard VBS state, the hidden Z2*Z2 symmetry breaks down when S is odd but remains unbroken when S is even. His results for partially dimerized VBS states suggest that the hidden Z2*Z2 symmetry breaking can be used to detect the successive dimerization transitions predicted by Affleck and Haldane (1987). Some new anisotropic VBS-type states are investigated. The result suggests that there are successive phase transitions when he increases 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 XXZ model and the magnetization process of antiferromagnets is investigated. He introduces an extended string order parameter which possesses a characteristic behavior in the partially dimerized VBS states.