Yuan-Ming Lu, Ashvin Vishwanath
We study topological phases of interacting systems in two spatial dimensions in the absence of topological order (i.e. unique ground state on closed manifolds, no fractional excitations). These are the closest interacting analogs of integer quantum Hall states and topological insulators and superconductors. We adapt the well-known Chern-Simons K-matrix description of quantum Hall states to classify such 'integer' topological phases. Our main result is a general formalism that incorporates symmetries into the {K}-matrix description. By combining distinct ways to realize symmetry with an analysis of edge stability, a variety of topological phases are determined. Remarkably, this simple analysis yields the same list of topological phases as a recent Borel cohomology classification, and in addition provides field theories and explicit edge theories for all these phases. The bosonic topological phases, which only appear in the presence of interactions, include insulators with quantized Hall conductance and bosonic analogs of quantum spin Hall insulators and chiral superconductors. We also discuss interacting fermion systems where symmetries are realized in a projective fashion, where we find the present formalism can handle a wider range of symmetries than a recent super-cohomology classification. Lastly we construct microscopic models of these phases from coupled one dimensional systems.
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http://arxiv.org/abs/1205.3156
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