The classification of symmetry protected topological phases of one-dimensional fermion systems

Chris Bourne, Yoshiko Ogata

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

We introduce an index for symmetry-protected topological (SPT) phases of infinite fermionic chains with an on-site symmetry given by a finite group G. This index takes values in with a generalised Wall group law under stacking. We show that this index is an invariant of the classification of SPT phases. When the ground state is translation invariant and has reduced density matrices with uniformly bounded rank on finite intervals, we derive a fermionic matrix product representative of this state with on-site symmetry.

Original languageEnglish
Article numbere25
JournalForum of Mathematics, Sigma
DOIs
Publication statusAccepted/In press - 2021

ASJC Scopus subject areas

  • Analysis
  • Theoretical Computer Science
  • Algebra and Number Theory
  • Statistics and Probability
  • Mathematical Physics
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Mathematics

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