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Title: Topological field theory and matrix product states

Abstract

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

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:
1425379
Alternate Identifier(s):
OSTI ID: 1374935
Grant/Contract Number:  
SC0011632
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 96; Journal Issue: 7; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Topological field theories; topological phases of matter; strongly correlated systems; topological materials; particles and fields; condensed matter and materials physics

Citation Formats

Kapustin, Anton, Turzillo, Alex, and You, Minyoung. Topological field theory and matrix product states. United States: N. p., 2017. Web. doi:10.1103/PhysRevB.96.075125.
Kapustin, Anton, Turzillo, Alex, & You, Minyoung. Topological field theory and matrix product states. United States. doi:10.1103/PhysRevB.96.075125.
Kapustin, Anton, Turzillo, Alex, and You, Minyoung. Mon . "Topological field theory and matrix product states". United States. doi:10.1103/PhysRevB.96.075125. https://www.osti.gov/servlets/purl/1425379.
@article{osti_1425379,
title = {Topological field theory and matrix product states},
author = {Kapustin, Anton and Turzillo, Alex and You, Minyoung},
abstractNote = {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},
doi = {10.1103/PhysRevB.96.075125},
journal = {Physical Review B},
number = 7,
volume = 96,
place = {United States},
year = {2017},
month = {8}
}

Journal Article:
Free Publicly Available Full Text
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Cited by: 2 works
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Figures / Tables:

Figure 1 Figure 1: An MPS represented as a tensor network

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Works referenced in this record:

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