Fermionic symmetry protected topological phases and cobordisms
Abstract
It has been proposed recently that interacting Symmetry Protected Topological Phases can be classified using cobordism theory. We test this proposal in the case of Fermionic SPT phases with \( {\mathrm{\mathbb{Z}}}_2 \) symmetry, where \( {\mathrm{\mathbb{Z}}}_2 \) is either timereversal or an internal symmetry. We find that cobordism classification correctly describes all known Fermionic SPT phases in space dimension D ≤ 3 and also predicts that all such phases can be realized by free fermions. In higher dimensions we predict the existence of inherently interacting fermionic SPT phases
 Authors:

 California Inst. of Technology (CalTech), Pasadena, CA (United States)
 Univ. of California, Berkeley, 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)
 OSTI Identifier:
 1599360
 Grant/Contract Number:
 SC0011632; FG0292ER40701
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of High Energy Physics (Online)
 Additional Journal Information:
 Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2015; Journal Issue: 12; Journal ID: ISSN 10298479
 Publisher:
 Springer Berlin
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Topological Field Theories; Effective field theories; Topological States of Matter
Citation Formats
Kapustin, Anton, Thorngren, Ryan, Turzillo, Alex, and Wang, Zitao. Fermionic symmetry protected topological phases and cobordisms. United States: N. p., 2015.
Web. doi:10.1007/JHEP12(2015)052.
Kapustin, Anton, Thorngren, Ryan, Turzillo, Alex, & Wang, Zitao. Fermionic symmetry protected topological phases and cobordisms. United States. https://doi.org/10.1007/JHEP12(2015)052
Kapustin, Anton, Thorngren, Ryan, Turzillo, Alex, and Wang, Zitao. Thu .
"Fermionic symmetry protected topological phases and cobordisms". United States. https://doi.org/10.1007/JHEP12(2015)052. https://www.osti.gov/servlets/purl/1599360.
@article{osti_1599360,
title = {Fermionic symmetry protected topological phases and cobordisms},
author = {Kapustin, Anton and Thorngren, Ryan and Turzillo, Alex and Wang, Zitao},
abstractNote = {It has been proposed recently that interacting Symmetry Protected Topological Phases can be classified using cobordism theory. We test this proposal in the case of Fermionic SPT phases with \( {\mathrm{\mathbb{Z}}}_2 \) symmetry, where \( {\mathrm{\mathbb{Z}}}_2 \) is either timereversal or an internal symmetry. We find that cobordism classification correctly describes all known Fermionic SPT phases in space dimension D ≤ 3 and also predicts that all such phases can be realized by free fermions. In higher dimensions we predict the existence of inherently interacting fermionic SPT phases},
doi = {10.1007/JHEP12(2015)052},
journal = {Journal of High Energy Physics (Online)},
number = 12,
volume = 2015,
place = {United States},
year = {2015},
month = {12}
}
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