Landau-Ginzburg Theories for Non-Abelian Quantum Hall States

Details Landau-Ginzburg Theories for Non-Abelian Quantum Hall States Landau-Ginzburg Theories for Non-Abelian Quantum Hall States

1998-11-02

arxiv.org/abs/cond-mat/9811005v1

Nucl.Phys. B546 (1999) 711-730

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

11 pages

Scientific paper

10.1016/S0550-3213(99)00039-5

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 $\nu=1$, 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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