2012/05/31 by Yuan-Ming Lu, Ashvin Vishwanath · 1 voice · 12 citations
Materials Science · Physics and Astronomy · #Chemical and Physical Properties of Materials #Cohomology #Homogeneous space #Quantum Hall effect #Quantum and electron transport phenomena #Symmetry protected topological order #Topological Materials and Phenomena #Topological degeneracy #Topological entropy in physics #Topological order #Topological quantum field theory #Topology (electrical circuits) #cond-mat.str-el #quant-ph
paper · pdf · doi:10.1103/physrevb.86.125119
published as Phys. Rev. B 86, 125119 (2012) · Published version with some errors and typos corrected
openalex publication_date 2012/09/14 · arxiv created 2014/05/13 · arxiv updated 2014/05/15 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We study topological phases of interacting systems in two spatial dimensions in the absence of topological order (i.e., with a unique ground state on closed manifolds and no fractional excitations). These are the closest interacting analogs of integer quantum Hall states, 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. Remarkably, this simple analysis yields the same list of topological phases as a recent group 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 and which remain well defined in the presence of disorder, include (i) bosonic insulators with a Hall conductance quantized to even integers, (ii) a bosonic analog of quantum spin Hall insulators, and (iii) a bosonic analog of a chiral topological superconductor, whose K matrix is the Cartan matrix of Lie group E8. 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 group super-cohomology classification. Lastly, we construct microscopic models of these phases from coupled one-dimensional systems.