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 v = 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.
- Landau-Ginzburg theory
- Non-abelian statistics
- Quantum Hall effect
ASJC Scopus subject areas
- Nuclear and High Energy Physics