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arXiv · 0812.0381

Collective states of non-abelian quasiparticles in a magnetic field

Michael Levin·Bertrand I. Halperin
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Abstract

Motivated by the physics of the Moore-Read ν= 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.

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Michael Levin, Bertrand I. Halperin. 2009-06-17. Collective states of non-abelian quasiparticles in a magnetic field. https://doi.org/10.1103/physrevb.79.205301

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