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

TL;DR

This study investigates the ground state properties of an $S=2$ quantum antiferromagnetic chain with bond alternation, revealing hidden symmetry breaking and successive dimerization transitions consistent with theoretical predictions.

Contribution

The paper provides the first quantum Monte Carlo evidence of hidden $Z_2 imes Z_2$ symmetry breaking and dimerization transitions in $S=2$ chains, confirming longstanding theoretical predictions.

Findings

Hidden $Z_2 imes Z_2$ symmetry is broken for $0.3 < | ext{delta}| < 0.5$

Successive dimerization transitions are confirmed in $S=2$ chains

Generalized string correlation behavior matches Valence-Bond-Solid state predictions

Abstract

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.