Classification of (2 + 1)D invertible fermionic topological phases with symmetry
Abstract
Here we provide a classification of invertible topological phases of interacting fermions with symmetry in two spatial dimensions for general fermionic symmetry groups Gf and general values of the chiral central charge c-. Here Gf is a central extension of a bosonic symmetry group Gb by fermion parity, (-1)F, specified by a second cohomology class [ω2]∈ $$\mathscr{H}^2$$(Gb,$$\mathbb{Z}_2$$). Our approach proceeds by gauging fermion parity and classifying the resulting Gb symmetry-enriched topological orders while keeping track of certain additional data and constraints. We perform this analysis through two perspectives, using G-crossed braided tensor categories and Spin(2c-)1 Chern-Simons theory coupled to a background G gauge field. These results give a way to characterize and classify invertible fermionic topological phases in terms of a concrete set of data and consistency equations, which is more physically transparent and computationally simpler than the more abstract methods using cobordism theory and spectral sequences. Our results also generalize and provide a different approach to the recent classification of fermionic symmetry-protected topological phases by Wang and Gu, which have chiral central charge c- = 0. We show how the tenfold way classification of topological insulators and superconductors fits into our scheme, along with general nonperturbative constraints due to certain choices of c- and Gf. Mathematically, our results also suggest an explicit general parametrization of deformation classes of (2 + 1)D invertible topological quantum field theories with Gf symmetry.
- Authors:
-
[1];
[2];
- University of Maryland, College Park, MD (United States)
- California Institute of Technology (CalTech), Pasadena, CA (United States)
- Publication Date:
- Research Org.:
- California Institute of Technology (CalTech), Pasadena, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP); National Science Foundation (NSF); University of Maryland; Simons Foundation
- OSTI Identifier:
- 1979768
- Grant/Contract Number:
- SC0011632; DMR-1753240
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. B
- Additional Journal Information:
- Journal Volume: 105; Journal Issue: 23; Journal ID: ISSN 2469-9950
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 36 MATERIALS SCIENCE; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Chern-Simons gauge theory; integer quantum Hall effect; Majorana fermions; quantum Hall effect; quantum spin Hall effect; symmetry protected topological states; topological field theories; topological insulators
Citation Formats
Barkeshli, Maissam, Chen, Yu-An, Hsin, Po-Shen, and Manjunath, Naren. Classification of (2 + 1)D invertible fermionic topological phases with symmetry. United States: N. p., 2022.
Web. doi:10.1103/physrevb.105.235143.
Barkeshli, Maissam, Chen, Yu-An, Hsin, Po-Shen, & Manjunath, Naren. Classification of (2 + 1)D invertible fermionic topological phases with symmetry. United States. https://doi.org/10.1103/physrevb.105.235143
Barkeshli, Maissam, Chen, Yu-An, Hsin, Po-Shen, and Manjunath, Naren. Wed .
"Classification of (2 + 1)D invertible fermionic topological phases with symmetry". United States. https://doi.org/10.1103/physrevb.105.235143. https://www.osti.gov/servlets/purl/1979768.
@article{osti_1979768,
title = {Classification of (2 + 1)D invertible fermionic topological phases with symmetry},
author = {Barkeshli, Maissam and Chen, Yu-An and Hsin, Po-Shen and Manjunath, Naren},
abstractNote = {Here we provide a classification of invertible topological phases of interacting fermions with symmetry in two spatial dimensions for general fermionic symmetry groups Gf and general values of the chiral central charge c-. Here Gf is a central extension of a bosonic symmetry group Gb by fermion parity, (-1)F, specified by a second cohomology class [ω2]∈ $\mathscr{H}^2$(Gb,$\mathbb{Z}_2$). Our approach proceeds by gauging fermion parity and classifying the resulting Gb symmetry-enriched topological orders while keeping track of certain additional data and constraints. We perform this analysis through two perspectives, using G-crossed braided tensor categories and Spin(2c-)1 Chern-Simons theory coupled to a background G gauge field. These results give a way to characterize and classify invertible fermionic topological phases in terms of a concrete set of data and consistency equations, which is more physically transparent and computationally simpler than the more abstract methods using cobordism theory and spectral sequences. Our results also generalize and provide a different approach to the recent classification of fermionic symmetry-protected topological phases by Wang and Gu, which have chiral central charge c- = 0. We show how the tenfold way classification of topological insulators and superconductors fits into our scheme, along with general nonperturbative constraints due to certain choices of c- and Gf. Mathematically, our results also suggest an explicit general parametrization of deformation classes of (2 + 1)D invertible topological quantum field theories with Gf symmetry.},
doi = {10.1103/physrevb.105.235143},
journal = {Physical Review. B},
number = 23,
volume = 105,
place = {United States},
year = {Wed Jun 29 00:00:00 EDT 2022},
month = {Wed Jun 29 00:00:00 EDT 2022}
}
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