Bulk-boundary correspondence for three-dimensional symmetry-protected topological phases

C Wang, CH Lin, M Levin - Physical Review X, 2016 - APS
C Wang, CH Lin, M Levin
Physical Review X, 2016APS
We derive a bulk-boundary correspondence for three-dimensional (3D) symmetry-protected
topological phases with unitary symmetries. The correspondence consists of three equations
that relate bulk properties of these phases to properties of their gapped, symmetry-
preserving surfaces. Both the bulk and surface data appearing in our correspondence are
defined via a procedure in which we gauge the symmetries of the system of interest and then
study the braiding statistics of excitations of the resulting gauge theory. The bulk data are …
We derive a bulk-boundary correspondence for three-dimensional (3D) symmetry-protected topological phases with unitary symmetries. The correspondence consists of three equations that relate bulk properties of these phases to properties of their gapped, symmetry-preserving surfaces. Both the bulk and surface data appearing in our correspondence are defined via a procedure in which we gauge the symmetries of the system of interest and then study the braiding statistics of excitations of the resulting gauge theory. The bulk data are defined in terms of the statistics of bulk excitations, while the surface data are defined in terms of the statistics of surface excitations. An appealing property of these data is that it is plausibly complete in the sense that the bulk data uniquely distinguish each 3D symmetry-protected topological phase, while the surface data uniquely distinguish each gapped, symmetric surface. Our correspondence applies to any 3D bosonic symmetry-protected topological phase with finite Abelian unitary symmetry group. It applies to any surface that (1) supports only Abelian anyons and (2) has the property that the anyons are not permuted by the symmetries.
American Physical Society
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