Higher-order bosonic topological phases in spin models

Oleg Dubinkin, Taylor L. Hughes

Research output: Contribution to journalArticlepeer-review


We discuss an extension of higher-order topological phases to include bosonic systems. We present two spin models for a second-order topological phase protected by a global Z2×Z2 symmetry. One model is built from layers of an exactly solvable cluster model for a one-dimensional Z2×Z2 topological phase, while the other is built from more conventional spin couplings (XY or Heisenberg). These models host gapped, symmetry-protected topological phases on their edges, and corner modes that fall into a projective representation of the symmetry. Using Jordan-Wigner transformations we show that both our models are related to a bilayer of free Majorana fermions that form a fermionic second-order topological phase. We also discuss how our models can be extended to three dimensions to form a third-order topological phase.

Original languageEnglish (US)
Article number235132
JournalPhysical Review B
Issue number23
StatePublished - Jun 14 2019
Externally publishedYes

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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