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Title: Spin topological field theory and fermionic matrix product states

Journal Article · · Physical Review B
 [1];  [1];  [1]
  1. California Inst. of Technology (CalTech), Pasadena, CA (United States)
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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.

Research Organization:
California Institute of Technology (CalTech), Pasadena, CA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), High Energy Physics (HEP)
Grant/Contract Number:
SC0011632
OSTI ID:
1598281
Alternate ID(s):
OSTI ID: 1468856
Journal Information:
Physical Review B, Vol. 98, Issue 12; ISSN 2469-9950
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 17 works
Citation information provided by
Web of Science

References (17)

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
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
Symmetry-protected topological orders for interacting fermions: Fermionic topological nonlinear σ models and a special group supercohomology theory journal September 2014
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
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
Matrix product states and equivariant topological field theories for bosonic symmetry-protected topological phases in (1+1) dimensions text January 2016
Topological Field Theory and Matrix Product States text January 2016
Module categories, weak Hopf algebras and modular invariants preprint January 2001

Cited By (3)

Fermionic Matrix Product States and One-Dimensional Short-Range Entangled Phases with Anti-Unitary Symmetries text January 2017
Full Commuting Projector Hamiltonians of Interacting Symmetry-Protected Topological Phases of Fermions text January 2018
Free and Interacting Short-Range Entangled Phases of Fermions: Beyond the Ten-Fold Way text January 2018

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Related Subjects

36 MATERIALS SCIENCE
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY