A ParticleHoleSymmetric Model for a Paired Fractional Quantum Hall State in a Halffilled 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 MooreRead Pfaffian wave function. The generating Hamiltonian for the MooreRead Pfaffian is a purely threebody model that breaks particlehole symmetry and lacks other properties, such as dominate twobody repulsive interactions, expected from a physical model of the FQHE. We use exact diagonalization to study the low energy states of a more physical twobody generator model derived from the threebody model. We find that the twobody model exhibits the essential features expected from the MooreRead Pfaffian: pairing, nonAbelian anyon excitations, and a neutral fermion mode. The model also satisfies constraints expected for a physical model of the FQHE at halffilling because it is: short range, spatially decaying, particlehole symmetric, and supports a roton mode with a robust spectral gap in the thermodynamic limit. Hence, this twobody model offers a bridge between artificial threebody generator models for paired states and the physical Coulomb interaction and can be used to further explore properties of nonAbelian physics in the FQHE.
 Publication:

arXiv eprints
 Pub Date:
 November 2018
 DOI:
 10.48550/arXiv.1811.02646
 arXiv:
 arXiv:1811.02646
 Bibcode:
 2018arXiv181102646H
 Keywords:

 Condensed Matter  Strongly Correlated Electrons
 EPrint:
 11 pages, 11 figures, 3 appendices