Non-abelian statistics in paired quantum Hall states

Csaba Tőke, Jainendra Jain

K. T. Law

Eddy Ardonne, Peter Bouwknegt, Kareljan Schoutens

Parsa Bonderson

Kareljan Schoutens, Eddy Ardonne

It has long been known that, under the laws of quantum mechanics, particles in two spatial dimensions may exhibit non-abelian braid statistics. In this note we briefly discuss particular states of matter, so-called paired and clustered quantum Hall states, which offer a concrete realization of this scenario: quasi-holes over these quantum Hall states satisfy non-abelian braid statistics. The associated degeneracies have their origin in combinatorial properties of (para-)fermions in conformal field theory. We also discuss the exclusion statistics of edge excitations in these quantum Hall systems.

Eddy Ardonne, Peter Bouwknegt, Sathya Guruswamy +1 more

Two fundamental aspects of so-called non-Abelian quantum Hall states (the q-Pfaffian states and more general) are a (generalized) pairing of the participating electrons and the non-Abelian statistics of the quasihole excitations. In this paper, we show that these two aspects are linked by a duality relation, which can be made manifest by considering the K-matrices that describe the exclusion statistics of the fundamental excitations in these systems.