Landau-Ginzburg theories for nonAbelian quantum Hall states

Nov, 1998
11 pages
Published in:
  • Nucl.Phys.B 546 (1999) 711-730
e-Print:

Citations per year

1998200420102016202201234567
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)