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arXiv:cond-mat/9511122 · Physical Review Letters

Phase Diagram of S=1 Bond-AlternatingXXZChains

Atsuhiro Kitazawa, K. Nomura, Kiyomi Okamoto

Published May 20, 1996• 94 citations
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Abstract

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 $S$.

DOI
10.1103/physrevlett.76.4038

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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 \ensuremathΔ=0\ensuremath{\Delta}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0\ensuremathΔ=0 (pure XY line). The critical properties can be interpreted as the Ashkin-Teller type reflecting the hidden Z2\ifmmode×\else\texttimes\fiZ2{\mathrm{Z}}_{2}\ifmmode\times\else\texttimes\fi{}{\mathrm{Z}}_{2}Z2​\ifmmode×\else\texttimes\fiZ2​ symmetry. We make a conjecture on the phase diagram of the present model for arbitrary SSS.
The phase diagram of the spin-1 bond-alternating XXZ chain is studied numerically. This model is appropriate to study the VBS picture and the hidden Z_2\times 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 be interpreted as the Ashkin-Teller type reflecting the hidden Z_2\times 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.
The phase diagram of the spin-1 bond-alternating XXZ chain is studied numerically. This model is appropriate to study the VBS picture and the hidden Z_2\times Z_2 symmetry concerning to the Haldane gap problem. The possible phases are the ferromagnetic, the XY, 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\times 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.
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.
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We investigate the ground-state phase diagram of the S=12\mathrm{S}=\frac{1}{2}S=21​ two-leg XXZXXZXXZ spin-ladder system with an isotropic interchain coupling. In this model, there is the Berezinskii-Kosterlitz-Thouless transition which occurs at the XYXYXY-Haldane and XYXYXY-rung singlet phase boundaries. It was difficult to determine the transition line using traditional methods. We overcome this difficulty using the level spectroscopy method combined with the twisted boundary condition method, and we check the consistency. We find out that the phase boundary between XYXYXY phase and Haldane phase lies on $\ensuremath{\Delta}=0$ line. And we show that there exist two different XYXYXY phases, which we can distinguish investigating a XXXXXX correlation function.