Bosonic Short Range Entangled states Beyond Group Cohomology classification

Xu, Cenke; You, Yi-Zhuang

doi:10.48550/arxiv.1410.6486

Cited by 2 publications

(3 citation statements)

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“…69 that (a) the SPT orders (described by H d (G, R/Z)) and pure gauge anomalies in one lower dimension are directly related and (b) the topological orders and gravitational anomalies in one lower dimension are directly related. This suggests that the SPT orders beyond H d (G, R/Z) [16][17][18]31,59,62,63 and mixed gauge-gravity anomalies are closely related. 59 This line of thinking gives us a deeper understanding of generic SPT states.…”

Section: Constructing Pure and Mixed Spt States As Well As Ito Statesmentioning

confidence: 96%

“…Later, it was realized that there also exist time-reversal protected SPT states that are beyond the H d (G, R/Z) description. [16][17][18] We like to point out that there are many other ways to construct SPT states, which include Chern-Simons theories, 19,20 NLσMs of symmetric space, 16,[21][22][23][24][25] projective construction, [26][27][28] domain wall decoration, 29 stringnet, 18 layered construction, 17 higher gauge theories, [30][31][32] etc .…”

Section: A Gapped Quantum Liquid Without Topological Excitationsmentioning

confidence: 99%

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Construction of bosonic symmetry-protected-trivial states and their topological invariants viaG×SO(∞)nonlinearσmodels

Wen

2015

Phys. Rev. B

114

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It has been shown that the bosonic symmetry-protected-trivial (SPT) phases with pure gauge anomalous boundary can all be realized via nonlinear σ models (NLσ Ms) of the symmetry group G with various topological terms. Those SPT phases (called the pure SPT phases) can be classified by group cohomology H d (G,R/Z). But there are also SPT phases with mixed gauge-gravity anomalous boundary (which will be called the mixed SPT phases). Some of the mixed SPT states were also referred as the beyond-group-cohomology SPT states. In this paper, we show that those beyond-group-cohomology SPT states are actually within another type of group cohomology classification. More precisely, we show that both the pure and the mixed SPT phases can be realized by G × SO(∞) NLσ Ms with various topological terms. Through the group cohomology, we find that the set of our constructed SPT phases in d-dimensional space-time are described by (charge conservation and time-reversal symmetry), we find that the mixed SPT phases beyond,R/Z] are described by Z 2 in 3 + 1D, Z in 4 + 1D, 3Z 2 in 5 + 1D, and 4Z 2 in 6 + 1D. Our construction also gives us the topological invariants that fully characterize the corresponding SPT and iTO phases. Through several examples, we show how the universal physical properties of SPT phases can be obtained from those topological invariants.

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Section: Constructing Pure and Mixed Spt States As Well As Ito Statesmentioning

confidence: 96%

Section: A Gapped Quantum Liquid Without Topological Excitationsmentioning

confidence: 99%

Construction of bosonic symmetry-protected-trivial states and their topological invariants viaG×SO(∞)nonlinearσmodels

Wen

2015

Phys. Rev. B

114

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“…In particular, we focus on the instability of free fermionic SPT (fFSPT) states against interaction, and investigate their interaction reduced classifications. More exotic fermionic SPT states that can not be reduced from free fermion descriptions 28,47,48 are not discussed in this work. The interaction reduced classification of interacting fermionic SPT (iFSPT) states can be derived by making connection to bosonic SPT (BSPT) states with the same symmetry, 70 and we will argue that the classification of BSPT states implies the classification of their fermionic counterparts.…”

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confidence: 99%

Symmetry-protected topological states of interacting fermions and bosons

2014

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We study the classification for a large class of interacting fermionic and bosonic symmetry protected topological (SPT) states, focusing on the cases where interaction reduces the classification of free fermion SPT states. We define a SPT state as whether or not it is separated from the trivial state through a bulk phase transition, which is a general definition applicable to SPT states with or without spatial symmetries. We show that in all dimensions short range interactions can reduce the classification of free fermion SPT states, and we demonstrate these results by making connection between fermionic and bosonic SPT states. We first demonstrate that our formalism gives the correct classification for several known SPT states, with or without interaction, then we will generalize our method to SPT states that involve the spatial inversion symmetry.

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Bosonic Short Range Entangled states Beyond Group Cohomology classification

Cited by 2 publications

References 0 publications

Construction of bosonic symmetry-protected-trivial states and their topological invariants viaG×SO(∞)nonlinearσmodels

Construction of bosonic symmetry-protected-trivial states and their topological invariants viaG×SO(∞)nonlinearσmodels

Symmetry-protected topological states of interacting fermions and bosons

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