title: Distinct trivial phases protected by a point-group symmetry in quantum spin chains.
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.
authors.affiliation: Institute for Solid State Physics, University of Tokyo, Kashiwa 277-8581, Japan.
authors.forename: Yohei
authors.initials: Y
authors.lastname: Fuji
authors.affiliation: Max-Planck-Institut für Physik komplexer Systeme, D-01187 Dresden, Germany.
authors.forename: Frank
authors.initials: F
authors.lastname: Pollmann
authors.affiliation: Institute for Solid State Physics, University of Tokyo, Kashiwa 277-8581, Japan.
authors.forename: Masaki
authors.initials: M
authors.lastname: Oshikawa