Symmetry Protected Topological Phases, Anomalies, and Cobordisms: Beyond Group Cohomology
arXiv:1403.1467
Abstract
We propose that Symmetry Protected Topological Phases with a finite symmetry group G are classified by cobordism groups of the classifying space of G. This provides an explanation for the recent discovery of bosonic SPT phases which do not fit into the group cohomology classification. We discuss the connection of the cobordism classification of SPT phases to gauge and gravitational anomalies in various dimensions.
17 pages, latex. v2: typos fixed, a footnote on terminology added. v3: substantially reworked version which takes into account the possibility of a nontrivial thermal Hall response
References in corpus (3)
Cited by in corpus (43)
- Generalized Global Symmetries
- Fermionic Matrix Product States and One-Dimensional Topological Phases
- Anomalies of discrete symmetries in various dimensions and group cohomology
- Topological Holography: Towards a Unification of Landau and Beyond-Landau Physics
- Lecture Notes on Generalized Symmetries and Applications
- Global Anomalies on the Hilbert Space
- Anomalies and Symmetry Fractionalization
- Anomaly Obstructions to Symmetry Preserving Gapped Phases
- Classification of (2+1)D invertible fermionic topological phases with symmetry
- Bosonic Topological Insulators and Paramagnets: a view from cobordisms
- Anomalies of Non-Invertible Symmetries in (3+1)d
- Lieb-Schultz-Mattis anomalies as obstructions to gauging (non-on-site) symmetries
- Symmetry-protected sign problem and magic in quantum phases of matter
- Higher-group symmetry in finite gauge theory and stabilizer codes
- Real-space construction of crystalline topological superconductors and insulators in 2D interacting fermionic systems
- Exactly Solvable Lattice Hamiltonians and Gravitational Anomalies
- Global anomalies in 8d supergravity
- Lieb-Schultz-Mattis anomalies and web of dualities induced by gauging in quantum spin chains
- Cobordism and Deformation Class of the Standard Model
- Gravitational anomaly of 3+1 dimensional Z_2 toric code with fermionic charges and fermionic loop self-statistics
- Homotopical Foundations of Parametrized Quantum Spin Systems
- Higher-group symmetry of (3+1)D fermionic gauge theory: logical CCZ, CS, and T gates from higher symmetry
- An index for two-dimensional SPT states
- Effective field theories of topological crystalline insulators and topological crystals
- Symmetries and anomalies of Kitaev spin- models: Identifying symmetry-enforced exotic quantum matter
- Strongly correlated crystalline higher-order topological phases in two-dimensional systems: A coupled-wire study
- Gauging anomalous unitary operators
- Higgs-Confinement Transitions in QCD from Symmetry Protected Topological Phases
- A unified diagrammatic approach to topological fixed point models
- Exotic Invertible Phases with Higher-Group Symmetries
- Remarks on Berry Connection in QFT, Anomalies, and Applications
- Asymptotic safety, quantum gravity, and the swampland: a conceptual assessment
- Differential models for the Anderson dual to bordism theories and invertible QFT's, II
- Reflection Structures and Spin Statistics in Low Dimensions
- Characterization and Classification of Fermionic Symmetry Enriched Topological Phases
- Solvable lattice model for (2+1)D bosonic topological insulator
- Anomaly of -Dimensional Symmetry-Enriched Topological Order from -Dimensional Topological Quantum Field Theory
- Lieb-Robinson Bounds on Entanglement Gaps from Symmetry-Protected Topology
- Remote detectability from entanglement bootstrap I: Kirby's torus trick
- Fermionic defects of topological phases and logical gates
- Topological Dipole Insulator
- Tensor network representations of fermionic crystalline topological phases on two-dimensional lattices
- Anomaly-induced edge currents in hydrodynamics with parity anomaly