A composite particle construction of the Fibonacci fractional quantum Hall state

Abstract

The Fibonacci topological order is the simplest platform for a universal topological quantum computer, consisting of a single type of non-Abelian anyon, $\tau$, with fusion rule $\tau \times \tau =1+\tau$. While it has been proposed that the anyon spectrum of the $\nu =12/5$ fractional quantum Hall state includes a Fibonacci sector, a dynamical picture of how a pure Fibonacci state may emerge in a quantum Hall system has been lacking. Here we use recently proposed non-Abelian dualities to construct a Fibonacci state of bosons at filling $\nu =2$ starting from a trilayer of integer quantum Hall states. Our parent theory consists of bosonic "composite vortices" coupled to fluctuating $U(2)$ gauge fields, which is related to the standard theory of Laughlin quasiparticles by duality. The Fibonacci state is obtained by clustering the composite vortices between the layers, along with flux attachment, a procedure reminiscent of the clustering picture of the Read-Rezayi states. We further use this framework to motivate a wave function for the Fibonacci fractional quantum Hall state.

arXiv comment12 pages, 3 figures, and 5 appendices

References in corpus (43)

• Non-Abelian Anyons and Topological Quantum Computation
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
• Direct observation of anyonic braiding statistics at the $\nu$=1/3 fractional quantum Hall state
• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Chern-Simons Theory with Vector Fermion Matter
• Observation of half-integer thermal Hall conductance
• Condensate induced transitions between topologically ordered phases
• Universal topological quantum computation from a superconductor/Abelian quantum Hall heterostructure
• Detecting Non-Abelian Statistics in the nu=5/2 Fractional Quantum Hall State
• Towards identification of a non-abelian state: observation of a quarter of electron charge at $\nu =5/2$ quantum Hall state
• Proposed experiments to probe the non-abelian ν=5/2 quantum Hall state
• Level/rank Duality and Chern-Simons-Matter Theories
• Measurement of filling factor 5/2 quasiparticle interference: observation of charge e/4 and e/2 period oscillations
• d=3 Bosonic Vector Models Coupled to Chern-Simons Gauge Theories
• From Luttinger liquid to non-Abelian quantum Hall states
• A Chern-Simons Effective Field Theory for the Pfaffian Quantum Hall State
• Particle-Vortex Duality from 3d Bosonization
• Baryons, monopoles and dualities in Chern-Simons-matter theories
• New Class of Non-Abelian Spin-Singlet Quantum Hall States
• Magnetic field-tuned Aharonov-Bohm oscillations and evidence for non-Abelian anyons at v=5/2
• Two-Loop Analysis of Non-abelian Chern-Simons Theory
• The non-Abelian Interferometer
• Fibonacci anyons and charge density order in the 12/5 and 13/5 plateaus
• Realizing non-Abelian statistics
• Landau-Ginzburg Theories for Non-Abelian Quantum Hall States
• Fermionic Chern-Simons theory for the Fractional Quantum Hall Effect in Bilayers
• Effective Field Theory and Projective Construction for the Z_k Parafermion Fractional Quantum Hall States
• Parton construction of particle-hole-conjugate Read-Rezayi parafermion fractional quantum Hall states and beyond
• Non-Abelian 3d Bosonization and Quantum Hall States
• Fibonacci Topological Superconductor
• The enigmatic 12/5 fractional quantum Hall effect
• Separation of spin and charge in paired spin-singlet quantum Hall states
• Exceptional Chern-Simons-Matter Dualities
• Classification of Abelian and Non-Abelian Multilayer Fractional Quantum Hall States Through the Pattern of Zeros
• Non-Abelian bosonization and modular transformation approach to superuniversality
• Strong-Weak Chern-Simons-Matter Dualities from a Lattice Construction
• Simple-current algebra constructions of 2+1D topological orders
• Landau-Ginzburg Theories of Non-Abelian Quantum Hall States from Non-Abelian Bosonization
• A non-Abelian twist to integer quantum Hall states
• Chern-Simons-Higgs transitions out of Topological Superconducting Phases
• Non-Abelian Fermionization and the Landscape of Quantum Hall Phases
• Chiral topologically ordered insulating phases in arrays of interacting integer quantum Hall islands

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