Composite particle construction of the Fibonacci fractional quantum Hall state

Hart Goldman, Ramanjit Sohal, Eduardo Fradkin

Research output: Contribution to journalArticlepeer-review


The Fibonacci topological order is the simplest platform for a universal topological quantum computer. While the ν=12/5 fractional quantum Hall (QH) state has been proposed to support a Fibonacci sector, a dynamical picture of how a pure Fibonacci state may emerge in a QH system has been lacking. We use non-Abelian dualities to construct a Fibonacci state of bosons at filling ν=2 starting from a trilayer of integer QH states. Our parent theory consists of bosonic composite vortices coupled to fluctuating U(2) gauge fields, which is dual to the theory of Laughlin quasiparticles. The Fibonacci state is obtained by interlayer clustering of the composite vortices, along with flux attachment. We use this framework to motivate a wave function for the Fibonacci state.

Original languageEnglish (US)
Article number235118
JournalPhysical Review B
Issue number23
StatePublished - Jun 15 2021

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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