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

TL;DR

This paper investigates the nature of three-body correlations and finite-size effects in Moore-Read states on a sphere, revealing how short-range interactions influence the state’s properties and its relevance to experimental quantum Hall systems.

Contribution

It provides a detailed numerical analysis of three-body correlations in Moore-Read states, highlighting the impact of surface curvature and finite-size effects on their structure and excitations.

Findings

Moore-Read ground state has small overlaps with Coulomb eigenstates on a sphere.

Surface curvature affects the form of pair pseudopotential and correlations.

Moore-Read state is a more accurate model for experimental nu=5/2 states than previously thought.

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.