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Title: Spin topological field theory and fermionic matrix product states

Abstract

Here, we study state-sum constructions of G-equivariant spin topological quantum field theory (TQFTs) and their relationship to matrix product states. In the Neveu-Schwarz, Ramond, and twisted sectors, states of the TQFT are generalized matrix product states. Our findings are applied to the classification of fermionic short-range-entangled phases with a unitary symmetry G to determine the group law on the set of such phases. Interesting subtleties appear when the total symmetry group is a nontrivial extension of G by fermion parity.

Authors:
 [1];  [1];  [1]
  1. California Inst. of Technology (CalTech), Pasadena, CA (United States)
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:
1598281
Alternate Identifier(s):
OSTI ID: 1468856
Grant/Contract Number:  
[SC0011632]
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
[ Journal Volume: 98; Journal Issue: 12]; 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

Citation Formats

Kapustin, Anton, Turzillo, Alex, and You, Minyoung. Spin topological field theory and fermionic matrix product states. United States: N. p., 2018. Web. doi:10.1103/PhysRevB.98.125101.
Kapustin, Anton, Turzillo, Alex, & You, Minyoung. Spin topological field theory and fermionic matrix product states. United States. doi:10.1103/PhysRevB.98.125101.
Kapustin, Anton, Turzillo, Alex, and You, Minyoung. Tue . "Spin topological field theory and fermionic matrix product states". United States. doi:10.1103/PhysRevB.98.125101. https://www.osti.gov/servlets/purl/1598281.
@article{osti_1598281,
title = {Spin topological field theory and fermionic matrix product states},
author = {Kapustin, Anton and Turzillo, Alex and You, Minyoung},
abstractNote = {Here, we study state-sum constructions of G-equivariant spin topological quantum field theory (TQFTs) and their relationship to matrix product states. In the Neveu-Schwarz, Ramond, and twisted sectors, states of the TQFT are generalized matrix product states. Our findings are applied to the classification of fermionic short-range-entangled phases with a unitary symmetry G to determine the group law on the set of such phases. Interesting subtleties appear when the total symmetry group is a nontrivial extension of G by fermion parity.},
doi = {10.1103/PhysRevB.98.125101},
journal = {Physical Review B},
number = [12],
volume = [98],
place = {United States},
year = {2018},
month = {9}
}

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Cited by: 3 works
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Works referenced in this record:

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