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Title: State sum constructions of spin-TFTs and string net constructions of fermionic phases of matter

Abstract

It is possible to describe fermionic phases of matter and spin-topological field theories in 2+1d in terms of bosonic “shadow” theories, which are obtained from the original theory by “gauging fermionic parity”. Furthemore, the fermionic/spin theories are recovered from their shadow by a process of fermionic anyon condensation: gauging a one-form symmetry generated by quasi-particles with fermionic statistics. We apply the formalism to theories which admit gapped boundary conditions. We obtain Turaev-Viro-like and Levin-Wen-like constructions of fermionic phases of matter. Here, we describe the group structure of fermionic SPT phases protected by Z 2f × G. The quaternion group makes a surprise appearance.

Authors:
 [1];  [1];  [2]
  1. Perimeter Inst. for Theoretical Physics, Waterloo, ON (Canada)
  2. California Inst. of Technology (CalTech), Pasadena, CA (United States). Dept. of Physics
Publication Date:
Research Org.:
California Inst. of Technology (CalTech), Pasadena, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
OSTI Identifier:
1393477
Grant/Contract Number:
SC0011632
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 4; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Anomalies in Field and String Theories; Discrete Symmetries; Topological Field Theories; Topological States of Matter

Citation Formats

Bhardwaj, Lakshya, Gaiotto, Davide, and Kapustin, Anton. State sum constructions of spin-TFTs and string net constructions of fermionic phases of matter. United States: N. p., 2017. Web. doi:10.1007/JHEP04(2017)096.
Bhardwaj, Lakshya, Gaiotto, Davide, & Kapustin, Anton. State sum constructions of spin-TFTs and string net constructions of fermionic phases of matter. United States. doi:10.1007/JHEP04(2017)096.
Bhardwaj, Lakshya, Gaiotto, Davide, and Kapustin, Anton. Tue . "State sum constructions of spin-TFTs and string net constructions of fermionic phases of matter". United States. doi:10.1007/JHEP04(2017)096. https://www.osti.gov/servlets/purl/1393477.
@article{osti_1393477,
title = {State sum constructions of spin-TFTs and string net constructions of fermionic phases of matter},
author = {Bhardwaj, Lakshya and Gaiotto, Davide and Kapustin, Anton},
abstractNote = {It is possible to describe fermionic phases of matter and spin-topological field theories in 2+1d in terms of bosonic “shadow” theories, which are obtained from the original theory by “gauging fermionic parity”. Furthemore, the fermionic/spin theories are recovered from their shadow by a process of fermionic anyon condensation: gauging a one-form symmetry generated by quasi-particles with fermionic statistics. We apply the formalism to theories which admit gapped boundary conditions. We obtain Turaev-Viro-like and Levin-Wen-like constructions of fermionic phases of matter. Here, we describe the group structure of fermionic SPT phases protected by Z2f × G. The quaternion group makes a surprise appearance.},
doi = {10.1007/JHEP04(2017)096},
journal = {Journal of High Energy Physics (Online)},
number = 4,
volume = 2017,
place = {United States},
year = {Tue Apr 18 00:00:00 EDT 2017},
month = {Tue Apr 18 00:00:00 EDT 2017}
}

Journal Article:
Free Publicly Available Full Text
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Citation Metrics:
Cited by: 2works
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