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

Ken Shiozaki, Shinsei Ryu

Research output: Contribution to journalArticlepeer-review

20 Scopus citations

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.

Original languageEnglish (US)
Article number100
JournalJournal of High Energy Physics
Volume2017
Issue number4
DOIs
StatePublished - Apr 1 2017
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics

Keywords

  • Global Symmetries
  • Lattice Quantum Field Theory
  • Topological Field Theories
  • Topological States of Matter

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