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Journal of the Physical Society of Japan

Critical Properties ofS=1Bond-Alternating XXZ Chains and HiddenZ2×Z2Symmetry

Atsuhiro Kitazawa, K. Nomura

Published Dec 15, 1997• 64 citations
Publisher

Abstract

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 × Z 2 symmetry concerning to the Haldane gap problem. The possible phases are the ferromagnetic, the X Y , the Haldane, the dimer, and the Néel ones. The critical properties of this model can be interpreted as the Ashkin-Teller type reflecting the hidden Z 2 × 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-Néel and dimer-Néel). We determine the phase boundary and universality class using the recent developed techniques by the authors.

DOI
10.1143/jpsj.66.3944

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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 $\ensuremath{\Delta}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ (pure XY line). The critical properties can be interpreted as the Ashkin-Teller type reflecting the hidden ${\mathrm{Z}}_{2}\ifmmode\times\else\texttimes\fi{}{\mathrm{Z}}_{2}$ symmetry. We make a conjecture on the phase diagram of the present model for arbitrary SSS.
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×Z2Z_{2}\times Z_{2}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×Z2Z_{2}\times Z_{2}Z2​×Z2​ symmetry.
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