Exactly Solvable Hamiltonian for Non-Abelian Quasiparticles

TL;DR

This paper introduces an exactly solvable Hamiltonian model for non-Abelian quasiparticles in the fractional quantum Hall effect, providing evidence for their non-Abelian braid statistics and demonstrating adiabatic continuity with known models.

Contribution

The authors construct a new exactly solvable Hamiltonian using Haldane pseudopotentials that captures both quasiholes and quasiparticles with non-Abelian statistics, extending previous models.

Findings

Exact solutions for quasiholes and quasiparticles

Evidence of non-Abelian braid statistics for quasiparticles

Adiabatic continuity with the lowest Landau level Hamiltonian

Abstract

Particles obeying non-Abelian braid statistics have been predicted to emerge in the fractional quantum Hall effect. In particular, a model Hamiltonian with short-range three-body interaction ($\hat{V}^\text{Pf}_3$) between electrons confined to the lowest Landau level provides exact solutions for quasiholes, and thereby allows a proof of principle for the existence of quasiholes obeying non-Abelian braid statistics. We construct, in terms of two- and three- body Haldane pseudopotentials, a model Hamiltonian that can be solved exactly for both quasiholes and quasiparticles, and provide evidence of non-Abelian statistics for the latter as well. The structure of the quasiparticle states of this model is in agreement with that predicted by the bipartite composite-fermion model of quasiparticles with exact lowest Landau level projection. We further demonstrate adiabatic continuity for the ground state, the ordinary neutral excitation, and the topological exciton as we deform our model Hamiltonian continuously into the lowest Landau-level $\hat{V}^\text{Pf}_3$ Hamiltonian.