Critical properties of S=1 bond-alternating XXZ chains and hidden Z2xZ2 symmetry

Critical properties of the spin-1 bond-alternating XXZ chain are studied numerically. This model is appropriate to study the VBS picture and hidden Z(2) x Z(2) symmetry concerning to the Haldane gap problem. The possible phases are the ferromagnetic, the XY, the Haldane, the dimer, and the Neel ones. The critical properties of this model can he interpreted as the Ashkin-Teller type reflecting the hidden Z(2) x Z(2) symmetry. The phase transitions are of the Berezinskii-Kosterlitz-Thouless type (XY-Haldane and XY-dimer), of the 2D Gaussian type (Haldane-dimer), and of the 2D Ising type (Haldane-Neel and dimer-Neel). We determine the phase boundary and universality class using the recent developed techniques by the authors.