Application of the level spectroscopy to Haldane conjecture 2, 3

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 $S$ .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 $S$.

arXiv:cond-mat/9511122Physical Review LettersMay 20, 199694 citations

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