nd - m at . s ta t - m ec h ] 2 6 M ay 1 99 7 Phase Diagrams of S = 3 / 2 , 2 XXZ Spin Chains with Bond - Alternation

We study the phase diagram of S = 3/2 and S = 2 bond-alternating spin chains numerically. In previous papers, the phase diagram of S = 1 XXZ spin chain with bond-alternation was shown to reflect the hidden Z2 ×Z2 symmetry. But for the higher S Heisenberg spin chain, the successive dimerization transition occurs, and for anisotropic spin chains the phase structure will be more colorful than the S = 1 case. Using recently developed methods, we show directly that the phase structure of the anisotropic spin chains relates to the Z2 × Z2 symmetry. Typeset using REVTEX 1 Haldane predicted that the antiferromagnetic Heisenberg spin chain has different behaviors between integer and half odd integer spins [1]. For half odd integer spin cases, the ground state has gapless excitations and spin correlations decay in the power law. The ground state properties for half odd spin Heisenberg chains are the same ones of the S = 1/2 case. On the other hand for integer spin cases, the ground state is a singlet with finite excitation gap and the spin correlations decay exponentially. Another aspect for the Haldane gapped state was presented by Affleck et.al. [2]. They studied a special S = 1 SU(2) spin chain which has the property of the Haldane gap conjecture, and proposed valence bond solid (VBS) states. The S = 1 VBS state has the hidden antiferromagnetic structure. Later den Nijs and Rommelse [3] found the string order parameter as the order parameter for it. Using a non-local unitary transformation, Kennedy and Tasaki [4] showed that the broken symmetry of S = 1 Haldane gap systems is a Z2 × Z2 type. Nearly four-fold degenerate states of the system with open boundary conditions reflect the discrete symmetry. For the higher S cases, Oshikawa [5] showed that odd integer S VBS states break the hidden Z2×Z2 symmetry, while even integer S VBS states do not violate the hidden Z2 × Z2 symmetry, and considered the generalized string order parameters. He pointed out another possibilities for the broken symmetry of higher S cases. In our previous papers with Okamoto [6,7], we studied the S = 1 XXZ spin chains with the bond-alternation,