Phase diagram of S = 1 bond-alternating XXZ chains

Phase transitions between the XY, the dimer, and the Haldane phases of the spin-1 bond-alternating XXZ chain are studied numerically. By use of the “level spectroscopy” we overcome the difficulties in treating the Berezinskii-Kosterlitz-Thouless transition which occurs at the XY-dimer and XY-Haldane boundaries. We find that the XY-Haldane boundary lies just on Δ = 0 (pure XY line). The critical properties can be interpreted as the Ashkin-Teller type reflecting the hidden Z₂ × Z₂ symmetry. We make a conjecture on the phase diagram of the present model for arbitrary S.