  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.
