Tripartite Composite Fermion States

Abstract

The Read-Rezayi wave function is one of the candidates for the fractional quantum Hall effect at filling fraction $ν=2+\nicefrac{3}{5}$, and thereby also its hole conjugate at $2+\nicefrac{2}{5}$. We study a general class of "tripartite" composite fermion wave functions, which reduce to the Read-Rezayi ground state and quasiholes for appropriate quantum numbers, but also allow a construction of wave functions for quasiparticles and neutral excitations by analogy to the standard composite fermion theory. We present numerical evidence in finite systems that these trial wave functions capture well the low energy physics of a 4-body model interaction. We also compare the tripartite composite fermion wave functions with the exact Coulomb eigenstates at $2+\nicefrac{3}{5}$, and find reasonably good agreement. The ground state as well as several excited states of the 4-body interaction are seen to evolve adiabatically into the corresponding Coulomb states for N=15 particles. These results support the plausibility of the Read-Rezayi proposal for the $2+\nicefrac{2}{5}$ and $2+\nicefrac{3}{5}$ fractional quantum Hall effect. However, certain other proposals also remain viable, and further study of excitations and edge states will be necessary for a decisive establishment of the physical mechanism of these fractional quantum Hall states.

17 pages, 14 figures

References in corpus (9)

• Fractional Quantum Hall States and Jack Polynomials
• Experimental studies of the fractional quantum Hall effect in the first excited Landau level
• Fractional Quantum Hall Hierarchy and the Second Landau Level
• Fractional Quantum Hall Effect in the Second Landau Level
• Wavefunctions for topological quantum registers
• Role of exciton screening in the 7/3 fractional quantum Hall effect
• Second Generation of Composite Fermions in the Hamiltonian Theory
• Possible Anti-Pfaffian Pairing of Composite Fermions in the Lowest Landau Level
• Filling the Bose sea: symmetric quantum Hall edge states and affine characters

Cited by in corpus (25)

• Quantum Hall Physics - hierarchies and CFT techniques
• Wavefunctionology: The Special Structure of Certain Fractional Quantum Hall Wavefunctions
• Thirty Years of Composite Fermions and Beyond
• Competing states for the fractional quantum Hall effect in the 1/3-filled second Landau level
• The Fractional Quantum Hall States at $\nu =13/5$ and $12/5$ and their Non-Abelian Nature
• Fractional Quantum Hall Effect at $\nu =2+6/13$: The Parton Paradigm for the Second Landau Level
• Fractional Quantum Hall Effect at $\nu =2+4/9$
• A non-Abelian fractional quantum Hall state at $3/7$ filled Landau level
• Fractional quantum Hall effect with unconventional pairing in monolayer graphene
• Interacting composite fermions: Nature of the 4/5, 5/7, 6/7, and 6/17 fractional quantum Hall states
• Projective construction of the ${\mathbb{Z}}_k$ Read-Rezayi fractional quantum Hall states and their excitations on the torus geometry
• Splitting of Girvin-MacDonald-Platzman density wave and the nature of chiral gravitons in fractional quantum Hall effect
• Fingerprints of Composite Fermion Lambda Levels in Scanning Tunneling Microscopy
• Fractional quantum Hall effect of partons and the nature of the 8/17 state in the zeroth Landau level of bilayer graphene
• Unlocking new regimes in fractional quantum Hall effect with quaternions
• Non-Abelian $\nu =1/2$ quantum Hall state in ${\Gamma }_8$ Valence Band Hole Liquid
• Ordering the topological order in the fractional quantum Hall effect
• Fusion mechanism for quasiparticles and topological quantum order in the lowest Landau level
• Exactly Solvable Hamiltonian for Non-Abelian Quasiparticles
• Mean field approximations for short range four body interactions at $\nu =3/5$
• Universal properties of the FQH state from the topological entanglement entropy and disorder effects
• Conformal field theory construction for nonabelian hierarchy wave functions
• Interplay of superconducting, metallic, and crystalline states of composite fermions at $\nu =1/6$ in wide quantum wells
• Torus geometry eigenfunctions of an interacting multi-Landau level Hamiltonian
• Exploring Quantum Hall Physics at Ultra-Low Temperatures and at High Pressures