Quasiparticles and excitons for the Pfaffian quantum Hall state

TL;DR

This paper introduces new trial wave functions for quasiparticles and excitons in the Moore-Read Pfaffian quantum Hall state, demonstrating good agreement with exact states and matching theoretical counting predictions.

Contribution

It presents a novel construction of trial wave functions for excitations in the Pfaffian state using a symmetrized double layer composite fermion approach.

Findings

Counting of quasiparticle states matches conformal field theory predictions.

Trial wave functions have high overlaps with exact solutions.

Results support the CFT description of the Moore-Read state and its excitations.

Abstract

We propose trial wave functions for quasiparticle and exciton excitations of the Moore-Read Pfaffian fractional quantum Hall states, both for bosons and for fermions, and study these numerically. Our construction of trial wave functions employs a picture of the bosonic Moore-Read state as a symmetrized double layer composite fermion state. We obtain the number of independent angular momentum multiplets of quasiparticle and exciton trial states for systems of up to 20 electrons. We find that the counting for quasielectrons at large angular momentum on the sphere matches that expected from the CFT which describes the Moore-Read state's boundary theory. In particular, the counting for quasielectrons is the same as for quasiholes, in accordance with the idea that the CFT describing both sides of the FQH plateau should be the same. We also show that our trial wave functions have good overlaps with exact wave functions obtained using various interactions, including second Landau level Coulomb interactions and the 3-body delta interaction for which the Pfaffian states and their quasiholes are exact ground states. We discuss how these results relate to recent work by Sreejith et al. on a similar set of trial wave functions for excitations over the Pfaffian state as well as to earlier work by Hansson et al., which has produced trial wave functions for quasiparticles based on conformal field theory methods and by Bernevig and Haldane, which produced trial wave functions based on clustering properties and `squeezing'.