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Landau-Ginzburg Theories for Non-Abelian Quantum Hall States

Eduardo Fradkin·Chetan Nayak·Kareljan Schoutens
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Abstract

We construct Landau-Ginzburg effective field theories for fractional quantum Hall states -- such as the Pfaffian state -- which exhibit non-Abelian statistics. These theories rely on a Meissner construction which increases the level of a non-Abelian Chern-Simons theory while simultaneously projecting out the unwanted degrees of freedom of a concomitant enveloping Abelian theory. We describe this construction in the context of a system of bosons at Landau level filling factor $ν=1$, where the non-Abelian symmetry is a dynamically-generated SU(2) continuous extension of the discrete particle-hole symmetry of the lowest Landau level. We show how the physics of quasiparticles and their non-Abelian statistics arises in this Landau-Ginzburg theory. We describe its relation to edge theories -- where a coset construction plays the role of the Meissner projection -- and discuss extensions to other states.

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Eduardo Fradkin, Chetan Nayak, Kareljan Schoutens. 1998-11-02. Landau-Ginzburg Theories for Non-Abelian Quantum Hall States. https://doi.org/10.1016/s0550-3213(99)00039-5

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