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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 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}
}

Journal Article:

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Cited by: 17 works
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Works referenced in this record:

Module categories, weak Hopf algebras and modular invariants
journal, June 2003


Fermionic matrix product states and one-dimensional topological phases
journal, February 2017


Complete classification of one-dimensional gapped quantum phases in interacting spin systems
journal, December 2011


Classification of gapped symmetric phases in one-dimensional spin systems
journal, January 2011


Classifying quantum phases using matrix product states and projected entangled pair states
journal, October 2011


Riemann surfaces and spin structures
journal, January 1971

  • Atiyah, Michael F.
  • Annales scientifiques de l'École normale supérieure, Vol. 4, Issue 1
  • DOI: 10.24033/asens.1205

Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems
journal, March 2008


Matrix product states and equivariant topological field theories for bosonic symmetry-protected topological phases in (1+1) dimensions
journal, April 2017


Topological field theory and matrix product states
journal, August 2017


Topological phases of fermions in one dimension
journal, February 2011


Spin Tqfts and Fermionic Phases of Matter
conference, November 2016

  • Gaiotto, Davide; Kapustin, Anton
  • The Memorial Workshop Devoted to the 85th Birthday of V N Gribov, Gribov-85 Memorial Volume: Exploring Quantum Field Theory
  • DOI: 10.1142/9789813141704_0044

State sum construction of two-dimensional topological quantum field theories on spin surfaces
journal, April 2015


Spin TQFTs and fermionic phases of matter
journal, October 2016

  • Gaiotto, Davide; Kapustin, Anton
  • International Journal of Modern Physics A, Vol. 31, Issue 28n29
  • DOI: 10.1142/S0217751X16450445

Topological Field Theory and Matrix Product States
text, January 2016


Works referencing / citing this record: