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Fermion decoration construction of symmetry protected trivial orders for fermion systems with any symmetries $G_f$ and in any dimensions

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arxiv 1809.01112 v1 pith:SPTEAABJ submitted 2018-09-04 cond-mat.str-el

Tian Lan , Chenchang Zhu , Xiao-Gang Wen This is my paper · ORCID
classification cond-mat.str-el
keywords fermionsymmetrydecorationordersprotectedtrivialconstructiondimensions
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abstract

We use higher dimensional bosonization and fermion decoration to construct exactly soluble interacting fermion models to realize fermionic symmetry protected trivial (SPT) orders (which are also known as symmetry protected topological orders) in any dimensions and for generic fermion symmetries $G_f$, which can be a non-trivial $Z_2^f$ extension (where $Z_2^f$ is the fermion-number-parity symmetry). This generalizes the previous results from group superconhomology of Gu and Wen (arXiv:1201.2648), where $G_f$ is assumed to be a trivial $Z_2^f$ extension. We find that the SPT phases from fermion decoration construction can be described in a compact way using higher groups.

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Cited by 3 Pith papers

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