A Chern-Simons effective field theory for the Pfaffian quantum Hall state

1997/11/11 by Eduardo Fradkin, E. Fradkin, Chetan Nayak +3 · 12 citations
Mathematics · Physics and Astronomy · #Chern–Simons theory #Coupling constant #Effective field theory #Electron #Fractional quantum Hall effect #Gauge theory #Mathematical physics #Mathematics #Pfaffian #Physics #Physics of Superconductivity and Magnetism #Pure mathematics #Quantum Hall effect #Quantum and electron transport phenomena #Quantum field theory #Quantum mechanics #Quantum spin Hall effect #Quasiparticle #Theoretical physics #Topological Materials and Phenomena #cond-mat.mes-hall

paper · pdf · doi:10.1016/s0550-3213(98)00111-4

published as Nucl.Phys. B516 (1998) 704-718 · 10 pages, LaTeX, 3 eps figures

arxiv created 1997/11/11 · openalex publication_date 1998/04/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We present a low-energy effective field theory describing the universality class of the Pfaffian quantum Hall state. To arrive at this theory, we observe that the edge theory of the Pfaffian state of bosons at ν=1 is an SU(2)₂ Kac-Moody algebra. It follows that the corresponding bulk effective field theory is an SU(2) Chern-Simons theory with coupling constant k=2. The effective field theories for other Pfaffian states, such as the fermionic one at ν=1/2 are obtained by a flux-attachment procedure. We discuss the non-Abelian statistics of quasiparticles in the context of this effective field theory.

Citations

• Quantum field theory and the Jones polynomial
• Fractional quantum Hall effect and Chern-Simons gauge theories
• 2n-quasihole states realize 2n−1-dimensional spinor braiding statistics in paired quantum Hall states
• Nonabelions in the fractional quantum hall effect
• Classical and quantum conformal field theory

Cited by

• Theoretical investigation of edge reconstruction in theν=52and73fractional quantum Hall states
• Paired quantum Hall states on noncommutative two-tori
• Edge-induced qubit polarization in systems with Ising anyons
• Effective Chern–Simons theories of pfaffian and parafermionic quantum Hall states, and orbifold conformal field theories
• Plasma analogy and non-Abelian statistics for Ising-type quantum Hall states
• Telegraph noise and the Fabry-Perot quantum Hall interferometer
• Loop models, modular invariance, and three-dimensional bosonization
• Measuring topological order
• Fractional quantum Hall effect via holography: Chern-Simons, edge states and hierarchy
• Edge states and interferometers in the Pfaffian and anti-Pfaffian states of theν=52quantum Hall system
• Effective field theories for topological insulators by functional bosonization
• Fibonacci Anyons Versus Majorana Fermions: A Monte Carlo Approach to the Compilation of Braid Circuits in SU(2)k Anyon Models