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Classification of (3+1)D Bosonic Topological Orders: The Case When Pointlike Excitations Are All Bosons
Published 2018“…Furthermore, all such 3+1D topological orders can be realized by Dijkgraaf-Witten gauge theories.…”
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Symmetry-Protected Quantum Spin Hall Phases in Two Dimensions
Published 2013“…At an open boundary, the θ term becomes the Wess-Zumino-Witten term and consequently the boundary excitations are decoupled gapless left movers and right movers. …”
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Majorana zero-modes and topological phases of multi-flavored Jackiw-Rebbi model
Published 2014“…Our results also indicate that a single normalizable Majorana zero mode can be compatible with the cancellation of SU(2) Witten anomaly.…”
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Topological nonlinear σ -model, higher gauge theory, and a systematic construction of 3 + 1 D topological orders for boson systems
Published 2021“…X 8, 021074 (2018)2160-330810.1103/PhysRevX.8.021074], it is shown that, if K is a space with only nontrivial first homotopy group G, which is finite, then these topological nonlinear σ-models can already realize all 3+1D bosonic topological orders without emergent fermions, which are described by Dijkgraaf-Witten theory with gauge group π1(K)=G. Under the similar conjecture, we show that the 3+1D bosonic topological orders with emergent fermions can be realized by topological nonlinear σ-models with π1(K)= finite groups, π2(K)=Z2, and πn>2(K)=0. …”
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Two-dimensional symmetry-protected topological orders and their protected gapless edge excitations
Published 2012“…The order is nontrivial because we can prove that the one-dimensional (1D) system on the boundary must be gapless if the symmetry is not broken, which generalizes the gaplessness of Wess-Zumino-Witten model for Lie symmetry groups to any discrete symmetry groups. …”
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Topological nonlinear σ -model, higher gauge theory, and a systematic construction of 3 + 1 D topological orders for boson systems
Published 2022“…X 8, 021074 (2018)2160-330810.1103/PhysRevX.8.021074], it is shown that, if K is a space with only nontrivial first homotopy group G, which is finite, then these topological nonlinear σ-models can already realize all 3+1D bosonic topological orders without emergent fermions, which are described by Dijkgraaf-Witten theory with gauge group π1(K)=G. Under the similar conjecture, we show that the 3+1D bosonic topological orders with emergent fermions can be realized by topological nonlinear σ-models with π1(K)= finite groups, π2(K)=Z2, and πn>2(K)=0. …”
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Classifying gauge anomalies through symmetry-protected trivial orders and classifying gravitational anomalies through topological orders
Published 2013“…We refer to other kinds of gauge anomalies beyond Adler-Bell-Jackiw anomalies as non-ABJ gauge anomalies, which include Witten SU(2) global gauge anomalies. We introduce a notion of π-cohomology group, H[-d+1 over π](BG,R/Z), for the classifying space BG, which is an Abelian group and include Tor[H[superscript d+1](G,R/Z)] and topological cohomology group H[superscript d+1](BG,R/Z) as subgroups. …”
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Symmetry protected topological orders and the group cohomology of their symmetry group
Published 2014“…The boundary excitations of the nontrivial SPT phases are described by lattice nonlinear σ models with a nonlocal Lagrangian term that generalizes the Wess-Zumino-Witten term for continuous nonlinear σ models. As a result, the symmetry G must be realized as a non-on-site symmetry for the low-energy boundary excitations, and those boundary states must be gapless or degenerate. …”
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