Numerical Study of Hierarchical Hall Edge States on the Disk Geometry

Abstract

We present a detailed analysis of the exact numerical spectrum of up to ten interacting electrons in the first Landau level on the disk geometry. We study the edge excitations of the hierarchical plateaus and check the predictions of two relevant conformal field theories: the multi-component Abelian theory and the W-infinity minimal theory of the incompressible fluids. We introduce two new criteria for identifying the edge excitations within the low-lying states: the plot of their density profiles and the study of their overlaps with the Jain wave functions in a meaningful basis. We find that the exact bulk and edge excitations are very well reproduced by the Jain states; these, in turn, can be described by the multi-component Abelian conformal theory. Most notably, we observe that the edge excitations form sub-families of the low-lying states with a definite pattern, which is explained by the W-infinity minimal conformal theory. Actually, the two conformal theories are related by a projection mechanism whose effects are observed in the spectrum. Therefore, the edge excitations of the hierarchical Hall states are consistently described by the W-infinity minimal theory, within the finite-size limitations.

Revtex, 25 pages, 17 figures and 11 tables

Cited by in corpus (18)

• Thermal Transport in Chiral Conformal Theories and Hierarchical Quantum Hall States
• Primary-Filling e/3 Quasiparticle Interferometer
• How universal is the fractional-quantum-Hall edge Luttinger liquid?
• Formation of an Edge Striped Phase in Fractional Quantum Hall Systems
• Surface modes of ultracold atomic clouds with very large number of vortices
• Composite fermion theory of correlated electrons in semiconductor quantum dots in high magnetic fields
• Fractional-quantum-Hall edge electrons and Fermi statistics
• Analytic Coulomb matrix elements in the lowest Landau level in disk geometry
• Hamiltonian Formulation of the W-Infinity Minimal Models
• Semiconductor quantum dots in high magnetic fields: The composite-fermion view
• Jain States in a Matrix Theory of the Quantum Hall Effect
• Composite fermions from the algebraic point of view
• Numerical Test of Disk Trial Wave function for Half-Filled Landau Level
• Strongly correlated states of trapped ultracold fermions in deformed Landau levels
• Composite Fermion Wavefunctions Derived by Conformal Field Theory
• Matrix Effective Theories of the Fractional Quantum Hall effect
• Semiclassical Droplet States in Matrix Quantum Hall Effect
• Laminar flow of charged quantum fluids of the Calogero-Sutherland universality class