On Z2-indices for ground states of fermionic chains

Chris Bourne, Hermann Schulz-Baldes

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


For parity-conserving fermionic chains, we review how to associate Z2-indices to ground states in finite systems with quadratic and higher-order interactions as well as to quasifree ground states on the infinite CAR algebra. It is shown that the Z2-valued spectral flow provides a topological obstruction for two systems to have the same Z2-index. A rudimentary definition of a Z2-phase label for a class of parity-invariant and pure ground states of the one-dimensional infinite CAR algebra is also provided. Ground states with differing phase labels cannot be connected without a closing of the spectral gap of the infinite GNS Hamiltonian.

Original languageEnglish
Article number2050028
JournalReviews in Mathematical Physics
Issue number9
Publication statusPublished - 2020 Oct 1
Externally publishedYes


  • Topological phases of matter
  • operator algebras
  • spectral flow

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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