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We study an AFM Heisenberg S=2 quantum spin chain at T=0 with bothinteraction 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 forthe S=2 anisotropic phase diagram, implying different mechanisms of theemergence of the classical limit. One main AKLT-based scenario predicts theemergence of a cascade of phase transitions not seen in the S=1 case. Anotherscenario is in favor of an almost classical phase diagram for S=2; the S=1 casethen is very special with its dominant quantum effects. Numerical studies havenot been conclusive. Using the DMRG, the existence of hidden topological orderin the anisotropic S=2 chain is examined, as it distinguishes between theproposed scenarios. We show that the topological order is zero in thethermodynamical limit in all disordered phases, in particular in the new phaseinterposed between the Haldane and large-$D$ phases. This excludes theAKLT-model based scenario in favor of an almost classical phase diagram for the$S\leq 2$ spin chains.Comment: 9 pages, 9 eps figures, uses RevTeX, submitted to PR

physical review. b, condensed matter

Absence of string order in the anisotropic<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:mn /></mml:math>Heisenberg antiferromagnet

Absence of string order in the anisotropicS=2Heisenberg antiferromagnet