Interacting topological phases and quantum anomalies

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Abstract

We give a brief overview on interacting symmetry-protected topological (SPT) phases. In particular, we will focus on various cases where the classification of non-interacting fermionic systems breaks down in the presence of interactions. The examples include topological (and trivial) superconductors in one, two and three spatial dimensions, protected by various symmetries such as time-reversal, spin parity, and reflection symmetries. Common to these examples is the collapse of the non-interacting classification, where an integer classification (Z) at non-interacting level reduces to Z8 or Z16 in the presence of interactions. We make use of these examples to illustrate various approaches to interacting SPT phases.

Original languageEnglish (US)
Article number014009
JournalPhysica Scripta
Volume2015
Issue numberT164
DOIs
StatePublished - Dec 1 2015
Externally publishedYes
Event156th Nobel Symposium on New Forms of Matter: Topological Insulators and Superconductors - Lidingo, Sweden
Duration: Jun 12 2014Jun 15 2014

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics
  • Mathematical Physics
  • Condensed Matter Physics

Keywords

  • quantum anomalies
  • symmetry-protected topological phases
  • topological insulators
  • topological phases of matter
  • topological superconductors

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