Juven Wang, Xiao-Gang Wen
We introduce the notion of boundary degeneracy of topologically ordered states on a compact orientable spatial manifold with boundaries, and emphasize that it provides richer information than the bulk degeneracy. Beyond the bulk-edge correspondence, we find the ground state degeneracy of fully gapped edge states depends on boundary gapping conditions. We develop a quantitative description of different types of boundary gapping conditions by viewing them as different ways of non-fractionalized particle condensation on the boundary. This allows us to derive the ground state degeneracy formula in terms of boundary gapping conditions, which reveals the fusion algebra of fractionalized quasiparticles. We apply our results to Toric code and Levin-Wen string-net models. By measuring the boundary degeneracy on a cylinder, we predict Z_k gauge theory and U(1)_k x U(1)_k non-chiral fractional quantum hall state at even integer k can be experimentally distinguished. Our works refine definitions of symmetry protected topological order and intrinsic topological order.
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http://arxiv.org/abs/1212.4863
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