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:
-
- California Inst. 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)
- 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. https://doi.org/10.1103/PhysRevB.98.125101
Kapustin, Anton, Turzillo, Alex, and You, Minyoung. Tue .
"Spin topological field theory and fermionic matrix product states". United States. https://doi.org/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 = {Tue Sep 04 00:00:00 EDT 2018},
month = {Tue Sep 04 00:00:00 EDT 2018}
}
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Works referencing / citing this record:
Fermionic Matrix Product States and One-Dimensional Short-Range Entangled Phases with Anti-Unitary Symmetries
text, January 2017
- Turzillo, Alex; You, Minyoung
- arXiv
Full Commuting Projector Hamiltonians of Interacting Symmetry-Protected Topological Phases of Fermions
text, January 2018
- Tantivasadakarn, Nathanan; Vishwanath, Ashvin
- arXiv
Free and Interacting Short-Range Entangled Phases of Fermions: Beyond the Ten-Fold Way
text, January 2018
- Chen, Yu-An; Kapustin, Anton; Turzillo, Alex
- arXiv