Three-body correlations and finite-size effects in the Moore--Read states on a sphere

Abstract

Two- and three-body correlations in partially filled degenerate fermion shells are studied numerically for various interactions between the particles. Three distinct correlation regimes are defined, depending on the short-range behavior of the pair pseudopotential. For pseudopotentials similar to those of electrons in the first excited Landau level, correlations at half-filling have a simple three-body form consisting of the maximum avoidance of the triplet state with the smallest relative angular momentum R_3=3. In analogy to the superharmonic criterion for Laughlin two-body correlations, their occurrence is related to the form of the three-body pseudopotential at short range. The spectra of a model three-body repulsion are calculated, and the zero-energy Moore--Read ground state, its +-e/4-charged quasiparticles, and the magnetoroton and pair-breaking bands are all identified. The quasiparticles are correctly described by a composite fermion model appropriate for Halperin's p-type pairing with Laughlin correlations between the pairs. However, the Moore--Read ground state, and specially its excitations, have small overlaps with the corresponding Coulomb eigenstates when calculated on a sphere. The reason lies in surface curvature which affects the form of pair pseudopotential for which the "R_3>3" three-body correlations occur. In finite systems, such pseudopotential must be slightly superharmonic at short range (different from Coulomb pseudopotential). However, the connection with the three-body pseudopotential is less size-dependent, suggesting that the Moore--Read state and its excitations are a more accurate description for experimental nu=5/2 states than could be expected from previous calculations.

12 pages, 12 figures, submitted to PRB

References in corpus (8)

• Fractional Quantum Hall Effect of Composite Fermions
• Monte Carlo Evaluation of Non-Abelian Statistics
• Fractional Quantum Hall States of Clustered Composite Fermions
• Structures for Interacting Composite Fermions: Stripes, Bubbles, and Fractional Quantum Hall Effect
• Novel Families of Fractional Quantum Hall States: Pairing of Composite Fermions
• Electron correlations in a partially filled first excited Landau level
• Conductivity of Paired Composite Fermions
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Cited by in corpus (12)

• A nu=2/5 Paired Wavefunction
• Pseudopotentials for Multi-particle Interactions in the Quantum Hall Regime
• Transition from Abelian to non-Abelian quantum liquids in the second Landau level
• Landau level mixing in the nu=5/2 fractional quantum Hall state
• Emergence of Jack ground states from two-body pseudopotentials in fractional quantum Hall systems
• The Hierarchy of Incompressible Fractional Quantum Hall States
• Second Generation of Moore-Read Quasiholes in a Composite Fermion Liquid
• Pair-distribution functions of correlated composite fermions
• Fractional quantum Hall effect and electron correlations in partially filled first excited Landau level
• Phase diagram of compressible and paired states in the quarter-filled Landau level
• Excitations of the $\nu =5/2$ Fractional Quantum Hall State and the Generalized Composite Fermion Picture
• Search for electron liquids with non-Abelian quasiparticles