Exactly Solvable Hamiltonian for Non-Abelian Quasiparticles

Abstract

Particles obeying non-Abelian braid statistics have been predicted to emerge in the fractional quantum Hall effect. In particular, a model Hamiltonian with short-range three-body interaction (${\hat{V}}_3^{\text{Pf}}$) between electrons confined to the lowest Landau level provides exact solutions for quasiholes, and thereby allows a proof of principle for the existence of quasiholes obeying non-Abelian braid statistics. We construct, in terms of two- and three- body Haldane pseudopotentials, a model Hamiltonian that can be solved exactly for both quasiholes and quasiparticles, and provide evidence of non-Abelian statistics for the latter as well. The structure of the quasiparticle states of this model is in agreement with that predicted by the bipartite composite-fermion model of quasiparticles with exact lowest Landau level projection. We further demonstrate adiabatic continuity for the ground state, the ordinary neutral excitation, and the topological exciton as we deform our model Hamiltonian continuously into the lowest Landau-level ${\hat{V}}_3^{\text{Pf}}$ Hamiltonian.

arXiv comment15 pages, 10 figures

References in corpus (36)

• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Non-abelian statistics of half-quantum vortices in p-wave superconductors
• Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
• Topologically-Protected Qubits from a Possible Non-Abelian Fractional Quantum Hall State
• $2n$ Quasihole States Realize $2^{n-1}$-Dimensional Spinor Braiding Statistics in Paired Quantum Hall States
• Observation of half-integer thermal Hall conductance
• Transition from quantum Hall to compressible states in the second Landau level: new light on the $\nu$=5/2 enigma
• Proposed experiments to probe the non-abelian ν=5/2 quantum Hall state
• Measurement of filling factor 5/2 quasiparticle interference: observation of charge e/4 and e/2 period oscillations
• Quasiholes and fermionic zero modes of paired fractional quantum Hall states: the mechanism for nonabelian statistics
• Quantum Hall Physics - hierarchies and CFT techniques
• Composite Fermions in the Hilbert Space of the Lowest Electronic Landau Level
• A short introduction to Fibonacci anyon models
• Magnetic field-tuned Aharonov-Bohm oscillations and evidence for non-Abelian anyons at v=5/2
• Collective States of Interacting Anyons, Edge States, and the Nucleation of Topological Liquids
• Possibility of p-wave pairing of composite fermions at $\nu =1/2$
• Collective states of interacting Fibonacci anyons
• Interlayer fractional quantum Hall effect in a coupled graphene double-layer
• Evidence for pairing states of composite fermions in double-layer graphene
• Monte Carlo Evaluation of Non-Abelian Statistics
• Non-Abelian Parton Fractional Quantum Hall Effect in Multilayer Graphene
• Phase Diagram of Bilayer Composite Fermion States
• Neutral Fermion Excitations in the Moore-Read state at ν=5/2
• Collective states of non-abelian quasiparticles in a magnetic field
• Unpaired composite fermion, topological exciton, and zero mode
• Competing Topological Orders in the nu=12/5 Quantum Hall State
• Quantum Hall quasielectrons - Abelian and non-Abelian
• Experimental Demonstration of Fermi Surface Effects at Filling Factor 5/2
• Quasiparticles and excitons for the Pfaffian quantum Hall state
• Tripartite Composite Fermion States
• Condensing non-Abelian quasiparticles
• Direct observation of composite fermions and their fully spin-polarized Fermi sea near $\nu =5/2$
• Local two-body parent Hamiltonians for the entire Jain sequence
• The Jain-2/5 parent Hamiltonian: structure of zero modes, dominance patterns, and zero mode generators
• Bardeen-Cooper-Schrieffer pairing of composite fermions
• An Exactly Solvable Model for Strongly Interacting Electrons in a Magnetic Field

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