A Particle-Hole-Symmetric Model for Paired Fractional Quantum Hall States In a Half-filled Landau Level*

The fractional quantum Hall effect (FQHE) observed at half filling of the second Landau level is believed to be caused by a BCS-type 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 properties expected from a physical model. 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 has a roton mode with a robust spectral gap in the thermodynamic limit. Hence, this two-body model offers a bridge between exact generator models of paired states and the physical Coulomb interaction and can be used to further explore properties of non-Abelian physics in the FQHE.