Hidden Z2×Z2 symmetry breaking in Haldane-gap antiferromagnets

Tom Kennedy and Hal Tasaki
Phys. Rev. B 45, 304 – Published 1 January 1992
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Abstract

We show that the Haldane phase of the S=1 antiferromagnetic chain is closely related to the breaking of a hidden Z2×Z2 symmetry. When the chain is in the Haldane phase, this Z2×Z2 symmetry is fully broken, but when the chain is in a massive phase other than the Haldane phase, e.g., the Ising phase or the dimerized phase, this symmetry is broken only partially or not at all. The hidden Z2×Z2 symmetry is revealed by introducing a nonlocal unitary transformation of the chain. This unitary transformation also leads to a simple variational calculation which qualitatively reproduces the phase diagram of the S=1 chain.

  • Received 29 July 1991

DOI:https://doi.org/10.1103/PhysRevB.45.304

©1992 American Physical Society

Authors & Affiliations

Tom Kennedy

  • Department of Mathematics, University of Arizona, Tucson, Arizona 85721

Hal Tasaki

  • Department of Physics, Gakushuin University, Mejiro, Toshima-ku, Tokyo 171, Japan

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Vol. 45, Iss. 1 — 1 January 1992

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