4,533 research outputs found

    Vortex-line condensation in three dimensions: A physical mechanism for bosonic topological insulators

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    Bosonic topological insulators (BTI) in three dimensions are symmetry-protected topological phases (SPT) protected by time-reversal and boson number conservation {symmetries}. BTI in three dimensions were first proposed and classified by the group cohomology theory which suggests two distinct root states, each carrying a Z2\mathbb{Z}_2 index. Soon after, surface anomalous topological orders were proposed to identify different root states of BTI, which even leads to a new BTI root state beyond the group cohomology classification. In this paper, we propose a universal physical mechanism via \textit{vortex-line condensation} {from} a 3d superfluid to achieve all {three} root states. It naturally produces bulk topological quantum field theory (TQFT) description for each root state. Topologically ordered states on the surface are \textit{rigorously} derived by placing TQFT on an open manifold, which allows us to explicitly demonstrate the bulk-boundary correspondence. Finally, we generalize the mechanism to ZNZ_N symmetries and discuss potential SPT phases beyond the group cohomology classification.Comment: ReVTeX 4.1 (published version

    Towards a complete classification of fermionic symmetry protected topological phases in 3D and a general group supercohomology theory

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    Classification and construction of symmetry protected topological (SPT) phases in interacting boson and fermion systems have become a fascinating theoretical direction in recent years. It has been shown that the (generalized) group cohomology theory or cobordism theory can give rise to a complete classification of SPT phases in interacting boson/spin systems. Nevertheless, the construction and classification of SPT phases in interacting fermion systems are much more complicated, especially in 3D. In this work, we revisit this problem based on the equivalent class of fermionic symmetric local unitary (FSLU) transformations. We construct very general fixed point SPT wavefunctions for interacting fermion systems. We naturally reproduce the partial classifications given by special group super-cohomology theory, and we show that with an additional B~H2(Gb,Z2)\tilde{B}H^2(G_b, \mathbb Z_2) (the so-called obstruction free subgroup of H2(Gb,Z2)H^2(G_b, \mathbb Z_2)) structure, a complete classification of SPT phases for three-dimensional interacting fermion systems with a total symmetry group Gf=GbΓ—Z2fG_f=G_b\times \mathbb Z_2^f can be obtained for unitary symmetry group GbG_b. We also discuss the procedure of deriving a general group super-cohomology theory in arbitrary dimensions.Comment: 48 pages, 35 figures, published versio
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