1998/11/02 by Eduardo Fradkin, Chetan Nayak, Kareljan Schoutens · 1 citation
Physics and Astronomy · #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #Topological Materials and Phenomena #cond-mat.mes-hall #cond-mat.str-el
paper · pdf · doi:10.1016/s0550-3213(99)00039-5
published as Nucl.Phys. B546 (1999) 711-730 · 11 pages
arxiv created 1998/11/02 · openalex publication_date 1999/05/01 · arxiv updated 2009/11/30 · openalex created_date 2020/11/23 · openalex updated_date 2026/07/28
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.