= Haldane phase
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The $S=1$ <Heisenberg antiferromagnet> chain realizes the <Haldane phase>: a gapped <symmetry-protected topological phase> with effective <spin one-half> degrees of freedom at open ends. <Time-reversal symmetry> is one possible protecting symmetry. Integer <spin> alone does not imply the same protected class: odd- and even-integer chains differ. The broader gap distinction is the <Haldane conjecture>.<Nobel Lecture: Topological quantum matter by F. Duncan M. Haldane>[Haldane, individual Nobel lecture, p. 040502-9, Fig. 8 and odd-integer versus even-integer distinction]{ref}
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