Partition Functions of Non-Abelian Quantum Hall States

Partition functions of edge excitations are obtained for non-Abelian Hall states in the second Landau level, such as the anti-Read–Rezayi state, the Bonderson–Slingerland hierarchy and the Wen non-Abelian fluid, as well as for the non-Abelian spin-singlet state. The derivation is straightforward and unique starting from the non-Abelian conformal field theory data and solving the modular invariance conditions. The partition functions provide a complete account of the excitation spectrum and are used to describe experiments of Coulomb blockade and thermopower.Partition functions of edge excitations are obtained for non-Abelian Hall states in the second Landau level, such as the anti-Read–Rezayi state, the Bonderson–Slingerland hierarchy and the Wen non-Abelian fluid, as well as for the non-Abelian spin-singlet state. The derivation is straightforward and unique starting from the non-Abelian conformal field theory data and solving the modular invariance conditions. The partition functions provide a complete account of the excitation spectrum and are used to describe experiments of Coulomb blockade and thermopower.

arXiv:1007.1732Journal of Physics A Mathematical and TheoreticalJan 20, 201122 citations

Thermoelectric characteristics of ${\mathbb Z}_k$ parafermion Coulomb islandsThermoelectric characteristics of ${\mathbb Z}_k$ parafermion Coulomb islands

Lachezar S. Georgiev

Using the explicit rational conformal field theory partition functions for the ${\mathbb Z}_k$ parafermion quantum Hall states on a disk we compute numerically the thermoelectric power factor for Coulomb-blockaded islands at finite temperature. We demonstrate that the power factor is rather sensitive to the neutral degrees of freedom and could eventually be used to distinguish experimentally between different quantum Hall states having identical electric properties. This might help us to confirm whether non-Abelian quasiparticles, such as the Fibonacci anyons, are indeed present in the experimentally observed quantum Hall states.Using the explicit rational conformal field theory partition functions for the ${\mathbb Z}_k$ parafermion quantum Hall states on a disk we compute numerically the thermoelectric power factor for Coulomb-blockaded islands at finite temperature. We demonstrate that the power factor is rather sensitive to the neutral degrees of freedom and could eventually be used to distinguish experimentally between different quantum Hall states having identical electric properties. This might help us to confirm whether non-Abelian quasiparticles, such as the Fibonacci anyons, are indeed present in the experimentally observed quantum Hall states.

arXiv:1601.07034Jan 26, 20160 citations

Non-Abelian quantum Hall states of fermions and bosons

N. Read

Bulletin of the American Physical SocietyMar 5, 20070 citations

Thermoelectric characteristics of

{\mathbb Z}_k

parafermion Coulomb islands

Using the explicit rational conformal field theory partition functions for the

{\mathbb Z}_k

parafermion quantum Hall states on a disk we compute numerically the thermoelectric power factor for Coulomb-blockaded islands at finite temperature. We demonstrate that the power factor is rather sensitive to the neutral degrees of freedom and could eventually be used to distinguish experimentally between different quantum Hall states having identical electric properties. This might help us to confirm whether non-Abelian quasiparticles, such as the Fibonacci anyons, are indeed present in the experimentally observed quantum Hall states.