Higher structures in matrix product states

Shuhei Ohyama, Shinsei Ryu

Research output: Contribution to journalArticlepeer-review


For a parameterized family of invertible states (short-range-entangled states) in (1+1) dimensions, we discuss a generalization of the Berry phase. Using translationally invariant, infinite matrix product states (MPSs), we introduce a gerbe structure, a higher generalization of complex line bundles, as an underlying mathematical structure describing topological properties of a parameterized family of MPSs. Furthermore, we introduce a generalization of a quantum mechanical inner product, which we call the "triple inner product,"defined for three matrix product states. The triple inner product proves to extract a topological invariant, the Dixmier-Douady class over the parameter space.

Original languageEnglish (US)
Article number115152
JournalPhysical Review B
Issue number11
StatePublished - Mar 15 2024

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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