Short-range entanglement and invertible field theories

Abstract

Quantum field theories with an energy gap can be approximated at long-range by topological quantum field theories. The same should be true for suitable condensed matter systems. For those with short range entanglement (SRE) the effective topological theory is invertible, and so amenable to study via stable homotopy theory. This leads to concrete topological invariants of gapped SRE phases which are finer than existing invariants. Computations in examples demonstrate their effectiveness.

59 pages, 13 figures; references added to v2

References in corpus (7)

• Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
• The Uncertainty of Fluxes
• Anomalies of discrete symmetries in various dimensions and group cohomology
• On the Classification of Topological Field Theories
• Bosonic Topological Insulators and Paramagnets: a view from cobordisms
• Quadratic functions in geometry, topology,and M-theory
• Spin Chern-Simons and Spin TQFTs

Cited by in corpus (17)

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• Lecture Notes on Generalized Symmetries and Applications
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• Lieb-Schultz-Mattis anomalies as obstructions to gauging (non-on-site) symmetries
• Tenfold Topology of Crystals: Unified classification of crystalline topological insulators and superconductors
• Exactly Solvable Lattice Hamiltonians and Gravitational Anomalies
• Real-space construction of crystalline topological superconductors and insulators in 2D interacting fermionic systems
• Classification of chiral fermionic CFTs of central charge $\le 16$
• Gravitational anomaly of 3+1 dimensional Z_2 toric code with fermionic charges and fermionic loop self-statistics
• (SPT-)LSM theorems from projective non-invertible symmetries
• Effective field theories of topological crystalline insulators and topological crystals
• Strongly correlated crystalline higher-order topological phases in two-dimensional systems: A coupled-wire study
• Symmetry fractionalization, mixed-anomalies and dualities in quantum spin models with generalized symmetries
• Anomaly of $(2+1)$-Dimensional Symmetry-Enriched Topological Order from $(3+1)$-Dimensional Topological Quantum Field Theory
• Remote detectability from entanglement bootstrap I: Kirby's torus trick
• Tensor network representations of fermionic crystalline topological phases on two-dimensional lattices
• Semisimple Field Theories Detect Stable Diffeomorphism