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  • Title: Distinct trivial phases protected by a point-group symmetry in quantum spin chains.
    Author: Fuji Y, Pollmann F, Oshikawa M.
    Journal: Phys Rev Lett; 2015 May 01; 114(17):177204. PubMed ID: 25978259.
    Abstract:
    The ground state of the S=1 antiferromagnetic Heisenberg chain belongs to the Haldane phase--a well-known example of the symmetry-protected topological phase. A staggered field applied to the S=1 antiferromagnetic chain breaks all the symmetries that protect the Haldane phase as a topological phase, reducing it to a trivial phase. That is, the Haldane phase is then connected adiabatically to an antiferromagnetic product state. Nevertheless, as long as the symmetry under site-centered inversion combined with a spin rotation is preserved, the phase is still distinct from another trivial phase. We demonstrate the existence of such distinct symmetry-protected trivial phases using a field-theoretical approach and numerical calculations. Furthermore, a general proof and a nonlocal order parameter are given in terms of a matrix-product state formulation.
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