A Particle-Hole-Symmetric Model for a Paired Fractional Quantum Hall State in a Half-filled Landau Level

Abstract

The fractional quantum Hall effect (FQHE) observed at half filling of the second Landau level is believed to be caused by a pairing of composite fermions captured by the Moore-Read Pfaffian wave function. The generating Hamiltonian for the Moore-Read Pfaffian is a purely three-body model that breaks particle-hole symmetry and lacks other properties, such as dominate two-body repulsive interactions, expected from a physical model of the FQHE. We use exact diagonalization to study the low energy states of a more physical two-body generator model derived from the three-body model. We find that the two-body model exhibits the essential features expected from the Moore-Read Pfaffian: pairing, non-Abelian anyon excitations, and a neutral fermion mode. The model also satisfies constraints expected for a physical model of the FQHE at half-filling because it is: short range, spatially decaying, particle-hole symmetric, and supports a roton mode with a robust spectral gap in the thermodynamic limit. Hence, this two-body model offers a bridge between artificial three-body generator models for paired states and the physical Coulomb interaction and can be used to further explore properties of non-Abelian physics in the FQHE.

arXiv comment11 pages, 11 figures, 3 appendices; Version 3 corrects a mislabeled Grant number in the Acknowledgments

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• Automatic design of Hamiltonians
• Fractional quantum Hall effect at the filling factor $\nu =5/2$
• Fractional quantum Hall effect from frustration-free Hamiltonians
• Model interactions for Pfaffian paired states based on Chern-Simons field theory description
• Mean field approximations for short range four body interactions at $\nu =3/5$
• Topological pairing of composite fermions via criticality