Characterizing Topological Order with Matrix Product Operators

Mehmet Burak Şahinoğlu (Korresp. Autor*in), Dominic Williamson, Nick Bultinck, Michaël Mariën, Jutho Haegeman, Norbert Schuch, Frank Verstraete

Veröffentlichungen: Beitrag in FachzeitschriftArtikelPeer Reviewed

Abstract

One of the most striking features of gapped quantum phases that exhibit topological order is the presence of long-range entanglement that cannot be detected by any local order parameter. The formalism of projected entangled-pair states is a natural framework for the parameterization of gapped ground state wavefunctions which allows one to characterize topological order in terms of the virtual symmetries of the local tensors that encode the wavefunction. In their most general form, these symmetries are represented by matrix product operators acting on the virtual level, which leads to a set of algebraic rules characterizing states with topological quantum order. This construction generalizes the concepts of G- and twisted injectivity; the corresponding matrix product operators encode all topological features of the theory and provide a complete picture of the ground state manifold on the torus. We show how the string-net models of Levin and Wen fit within this formalism and in doing so provide a particularly intuitive interpretation of the pentagon equation for F-symbols as the pulling of matrix product operators through the string-net tensor network. Our approach paves the way to finding novel topological phases beyond string nets and elucidates the description of topological phases in terms of entanglement Hamiltonians and edge theories.
OriginalspracheEnglisch
Seiten (von - bis)563–592
Seitenumfang30
FachzeitschriftAnnales Henri Poincare
Jahrgang22
Ausgabenummer2
Frühes Online-Datum7 Jan. 2021
DOIs
PublikationsstatusVeröffentlicht - Feb. 2021
Extern publiziertJa

ÖFOS 2012

  • 103036 Theoretische Physik
  • 103019 Mathematische Physik

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