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Title: Topological field theory and matrix product states

Journal Article · · Physical Review B
 [1];  [2];  [2]
  1. California Inst. of Technology (CalTech), Pasadena, CA (United States); California Institute of Technology
  2. California Inst. of Technology (CalTech), Pasadena, CA (United States)
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It is believed that most (perhaps all) gapped phases of matter can be described at long distances by topological quantum field theory (TQFT). On the other hand, it has been rigorously established that in 1+1d ground states of gapped Hamiltonians can be approximated by matrix product states (MPS). We show that the state-sum construction of 2d TQFT naturally leads to MPS in their standard form. In the case of systems with a global symmetry G, this leads to a classification of gapped phases in 1+1d in terms of Morita-equivalence classes of G-equivariant algebras. Nonuniqueness of the MPS representation is traced to the freedom of choosing an algebra in a particular Morita class. In the case of short-range entangled phases, we recover the group cohomology classification of SPT phases

Research Organization:
California Inst. of Technology (CalTech), Pasadena, CA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
Grant/Contract Number:
SC0011632
OSTI ID:
1425379
Alternate ID(s):
OSTI ID: 1374935
Journal Information:
Physical Review B, Journal Name: Physical Review B Journal Issue: 7 Vol. 96; ISSN 2469-9950; ISSN PRBMDO
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

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Cited By (3)

Fermionic matrix product states and one-dimensional short-range entangled phases with antiunitary symmetries journal January 2019
Fermionic Matrix Product States and One-Dimensional Short-Range Entangled Phases with Anti-Unitary Symmetries text January 2017
Spin topological field theory and fermionic matrix product states journal September 2018

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97
72
Topological field theories
topological phases of matter
strongly correlated systems
topological materials
particles and fields
condensed matter and materials physics