Collective states of non-abelian quasiparticles in a magnetic field

TL;DR

This paper explores collective states of non-abelian quasiparticles in a magnetic field, proposing new hierarchical incompressible liquids and analyzing their abelian or non-abelian nature.

Contribution

It introduces a series of hierarchical non-abelian states and shows their abelian properties, extending understanding of quasiparticle collective states.

Findings

Hierarchical states at filling fractions 8/17 and 7/13 are abelian.

Constructed candidate Wigner crystal states are abelian.

Hierarchical states derived from Moore-Read are non-abelian.

Abstract

Motivated by the physics of the Moore-Read \nu = 1/2 state away from half-filling, we investigate collective states of non-abelian e/4 quasiparticles in a magnetic field. We consider two types of collective states: incompressible liquids and Wigner crystals. In the incompressible liquid case, we construct a natural series of states which can be thought of as a non-abelian generalization of the Laughlin states. These states are associated with a series of hierarchical states derived from the Moore-Read state - the simplest of which occur at filling fraction 8/17 and 7/13. Interestingly, we find that the hierarchical states are abelian even though their parent state is non-abelian. In the Wigner crystal case, we construct two candidate states. We find that they, too, are abelian - in agreement with previous analysis.