Chern-Simons theory of multi-component quantum Hall systems

Abstract

The Chern-Simons approach has been widely used to explain fractional quantum Hall states in the framework of trial wave functions. In the present paper, we generalise the concept of Chern-Simons transformations to systems with any number of components (spin or pseudospin degrees of freedom), extending earlier results for systems with one or two components. We treat the density fluctuations by adding auxiliary gauge fields and appropriate constraints. The Hamiltonian is quadratic in these fields and hence can be treated as a harmonic oscillator Hamiltonian, with a ground state that is connected to the Halperin wave functions through the plasma analogy. We investigate several conditions on the coefficients of the Chern-Simons transformation and on the filling factors under which our model is valid. Furthermore, we discuss several singular cases, associated with symmetric states.

11 pages, shortened version, accepted for publication in Phys. Rev. B

References in corpus (8)

• The electronic properties of graphene
• Analysis of a SU(4) generalization of Halperin's wave function as an approach towards a SU(4) fractional quantum Hall effect in graphene sheets
• The plasma picture of the fractional quantum Hall effect with internal SU(K) symmetries
• Microscopic origin of the next generation fractional quantum Hall effect
• Second Generation of Composite Fermions in the Hamiltonian Theory
• Fermion Chern Simons Theory of Hierarchical Fractional Quantum Hall States
• On the self-similarity in quantum Hall systems
• The Tomonaga-Luttinger Model and the Chern-Simons Theory for the Edges of Multi-layer Fractional Quantum Hall Systems

Cited by in corpus (5)

• Fermionic Chern-Simons Theory of SU(4) Fractional Quantum Hall Effect
• Incompressible Even Denominator Fractional Quantum Hall States in the Zeroth Landau Level of Monolayer Graphene
• Dynamical Mass Generation of Composite Dirac Fermions and Fractional Quantum Hall Effects near Charge Neutrality in Graphene
• Collective excitations of fractional quantum Hall states in monolayer graphene
• Two-dimensional electron-hole system under the influence of the Chern-Simons gauge field created by the quantum point vortices