Landau-Ginzburg theories for nonAbelian quantum Hall states
Nov, 1998
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Abstract: (Elsevier)
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 Chem-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 = l , 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.- 73.40.Hm
- 73.20.Dx
- Non-abelian statistics
- Landau-Ginzburg theory
- Quantum Hall effect
- Landau-Ginzburg model
- Hall effect: fractional
- statistics: nonabelian
- Chern-Simons term
- symmetry: SU(2)
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