Absence of string order in the anisotropic S=2 Heisenberg antiferromagnet

TL;DR

This study investigates the presence of string order in the anisotropic S=2 Heisenberg antiferromagnetic chain at zero temperature, using DMRG, and finds no topological order, supporting a classical phase diagram over AKLT-based quantum scenarios.

Contribution

The paper provides numerical evidence that the anisotropic S=2 chain lacks hidden topological order, challenging AKLT-based quantum phase transition predictions.

Findings

No string order in the thermodynamic limit across all disordered phases.

Excludes AKLT-model based scenario for S=2 chains.

Supports an almost classical phase diagram for S=2 spin chains.

Abstract

We study an AFM Heisenberg S=2 quantum spin chain at T=0 with both interaction and on-site anisotropy, H = \sum_{i} {1/2}(S^{+}_{i}S^{-}_{i+1}+S^{-}_{i}S^{+}_{i+1}) +J^{z}S^{z}_{i}S^{z}_{i+1}+D(S^{z}_{i})^{2}. Contradictory scenarios exist for the S=2 anisotropic phase diagram, implying different mechanisms of the emergence of the classical limit. One main AKLT-based scenario predicts the emergence of a cascade of phase transitions not seen in the S=1 case. Another scenario is in favor of an almost classical phase diagram for S=2; the S=1 case then is very special with its dominant quantum effects. Numerical studies have not been conclusive. Using the DMRG, the existence of hidden topological order in the anisotropic S=2 chain is examined, as it distinguishes between the proposed scenarios. We show that the topological order is zero in the thermodynamical limit in all disordered phases, in particular in the new phase interposed between the Haldane and large-$D$ phases. This excludes the AKLT-model based scenario in favor of an almost classical phase diagram for the $S\leq 2$ spin chains.