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- W1489275627 abstract "In [Z.-X. Liu, M. Liu, X.-G. Wen, arXiv:1101.5680], we studied 8 gapped symmetric quantum phases in S=1 spin chains %/ladders which respect a discrete spin rotation $D_2 subset SO(3)$ and time reversal $T$ symmetries. In this paper, using a generalized approach, we study all the 16 possible gapped symmetric quantum phases of 1D integer spin systems with only $D_2+T$ symmetry. Those phases are beyond Landau symmetry breaking theory and cannot be characterized by local order parameters, since they do not break any symmetry. They correspond to 16 symmetry protected topological (SPT) orders. We show that all the 16 SPT orders can be fully characterized by the physical properties of the symmetry protected degenerate boundary states (end `spins') at the ends of a chain segment. So we can measure and distinguish all the 16 SPT orders experimentally. We also show that all these SPT orders can be realized in S=1 spin ladder models. The gapped symmetric phases protected by subgroups of $D_2+T$ are also studied. Again, all these phases can be distinguished by physically measuring their end `spins'." @default.
- W1489275627 created "2016-06-24" @default.
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- W1489275627 date "2011-11-29" @default.
- W1489275627 modified "2023-09-22" @default.
- W1489275627 title "Symmetry-protected topological orders of one-dimensional spin systems withD2+Tsymmetry" @default.
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- W1489275627 doi "https://doi.org/10.1103/physrevb.84.195145" @default.
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