Hidden Order and Dimerization Transition in $S=2$ Chains

Details Hidden Order and Dimerization Transition in $S=2$ Chains Hidden Order and Dimerization Transition in $S=2$ Chains

1996-04-17

arxiv.org/abs/cond-mat/9604107v1

J. Phys. Soc. Jpn. 65, 1562 (1996)

Physics

Condensed Matter

3 pages (LaTex with jpsj-style files (ftp://ftp.u-tokyo.ac.jp/pub/SOCIETY/JPSJ)) and 1 Postscript figure

Scientific paper

10.1143/JPSJ.65.1562

We study ground state properties of the $S=2$ quantum antiferromagnetic chain with a bond alternation \[ H = \sum_{j} [ 1 + \delta (-1)^j ] \mbox{\boldmath $S$}_{j} \cdot \mbox{\boldmath $S$}_{j+1} \] by a Quantum Monte Carlo calculation. We find that the hidden $Z_2 \times Z_2$ symmetry is broken for $0.3 < |\delta| < 0.5$ while it is unbroken in the other regions. This confirms the successive dimerization transitions first predicted by Affleck and Haldane. Our result shows that these transitions can be understood in terms of the hidden $Z_2 \times Z_2$ symmetry breaking, as was discussed using the Valence-Bond-Solid states. Furthermore, we find that the behavior of the generalized string correlation is qualitatively very similar to that in the Valence-Bond-Solid states, including the location of zeroes as a function of the angle parameter.

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