Matrix product states and equivariant topological field theories for bosonic symmetry-protected topological phases in (1+1) dimensions
Abstract Matrix Product States (MPSs) provide a powerful framework to study and classify gapped quantum phases — symmetry-protected topological (SPT) phases in particular — defined in one dimensional lattices. On the other hand, it is natural to expect that gapped quantum phases in the limit of zero...
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Online Access: | http://link.springer.com/article/10.1007/JHEP04(2017)100 |
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doaj-cfddb7f6bda247b982efc05ce2f216122020-11-25T00:27:51ZengSpringerOpenJournal of High Energy Physics1029-84792017-04-012017414710.1007/JHEP04(2017)100Matrix product states and equivariant topological field theories for bosonic symmetry-protected topological phases in (1+1) dimensionsKen Shiozaki0Shinsei Ryu1Department of Physics, University of Illinois at Urbana ChampaignJames Franck Institute and Kadanoff Center for Theoretical Physics, University of ChicagoAbstract Matrix Product States (MPSs) provide a powerful framework to study and classify gapped quantum phases — symmetry-protected topological (SPT) phases in particular — defined in one dimensional lattices. On the other hand, it is natural to expect that gapped quantum phases in the limit of zero correlation length are described by topological quantum field theories (TFTs or TQFTs). In this paper, for (1+1)-dimensional bosonic SPT phases protected by symmetry G, we bridge their descriptions in terms of MPSs, and those in terms of G-equivariant TFTs. In particular, for various topological invariants (SPT invariants) constructed previously using MPSs, we provide derivations from the point of view of (1+1) TFTs. We also discuss the connection between boundary degrees of freedom, which appear when one introduces a physical boundary in SPT phases, and “open” TFTs, which are TFTs defined on spacetimes with boundaries.http://link.springer.com/article/10.1007/JHEP04(2017)100Topological Field TheoriesTopological States of MatterGlobal SymmetriesLattice Quantum Field Theory |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Ken Shiozaki Shinsei Ryu |
spellingShingle |
Ken Shiozaki Shinsei Ryu Matrix product states and equivariant topological field theories for bosonic symmetry-protected topological phases in (1+1) dimensions Journal of High Energy Physics Topological Field Theories Topological States of Matter Global Symmetries Lattice Quantum Field Theory |
author_facet |
Ken Shiozaki Shinsei Ryu |
author_sort |
Ken Shiozaki |
title |
Matrix product states and equivariant topological field theories for bosonic symmetry-protected topological phases in (1+1) dimensions |
title_short |
Matrix product states and equivariant topological field theories for bosonic symmetry-protected topological phases in (1+1) dimensions |
title_full |
Matrix product states and equivariant topological field theories for bosonic symmetry-protected topological phases in (1+1) dimensions |
title_fullStr |
Matrix product states and equivariant topological field theories for bosonic symmetry-protected topological phases in (1+1) dimensions |
title_full_unstemmed |
Matrix product states and equivariant topological field theories for bosonic symmetry-protected topological phases in (1+1) dimensions |
title_sort |
matrix product states and equivariant topological field theories for bosonic symmetry-protected topological phases in (1+1) dimensions |
publisher |
SpringerOpen |
series |
Journal of High Energy Physics |
issn |
1029-8479 |
publishDate |
2017-04-01 |
description |
Abstract Matrix Product States (MPSs) provide a powerful framework to study and classify gapped quantum phases — symmetry-protected topological (SPT) phases in particular — defined in one dimensional lattices. On the other hand, it is natural to expect that gapped quantum phases in the limit of zero correlation length are described by topological quantum field theories (TFTs or TQFTs). In this paper, for (1+1)-dimensional bosonic SPT phases protected by symmetry G, we bridge their descriptions in terms of MPSs, and those in terms of G-equivariant TFTs. In particular, for various topological invariants (SPT invariants) constructed previously using MPSs, we provide derivations from the point of view of (1+1) TFTs. We also discuss the connection between boundary degrees of freedom, which appear when one introduces a physical boundary in SPT phases, and “open” TFTs, which are TFTs defined on spacetimes with boundaries. |
topic |
Topological Field Theories Topological States of Matter Global Symmetries Lattice Quantum Field Theory |
url |
http://link.springer.com/article/10.1007/JHEP04(2017)100 |
work_keys_str_mv |
AT kenshiozaki matrixproductstatesandequivarianttopologicalfieldtheoriesforbosonicsymmetryprotectedtopologicalphasesin11dimensions AT shinseiryu matrixproductstatesandequivarianttopologicalfieldtheoriesforbosonicsymmetryprotectedtopologicalphasesin11dimensions |
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1725338144325238784 |