Fermions, strings, and gauge fields in lattice spin models

Michael Levin, Xiao Gang Wen

Research output: Contribution to journalArticlepeer-review

117 Scopus citations


We investigate the general properties of lattice spin models with emerging fermionic excitations. We argue that fermions always come in pairs and their creation operator always has a stringlike structure with the newly created particles appearing at the end points of the string. The physical implication of this structure is that the fermions always couple to a nontrivial gauge field. We present exactly soluble examples of this phenomenon in two and three dimensions. Our analysis is based on an algebraic formula that relates the statistics of a lattice particle to the properties of its hopping operators. This approach has the advantage in that it works in any number of dimensions—unlike the flux-binding picture developed in fractional quantum Hall theory.

Original languageEnglish
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number24
StatePublished - 20 Jun 2003
Externally publishedYes

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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