Edge properties of principal fractional quantum Hall states in the cylinder geometry
arXiv:1207.3267 · doi:10.1103/PhysRevB.86.115214
Abstract
We study fractional quantum Hall states in the cylinder geometry with open boundaries. We focus on principal fermionic 1/3 and bosonic 1/2 fractions in the case of hard-core interactions. The gap behavior as a function of the cylinder radius is analyzed. By adding enough orbitals to allow for edge modes we show that it is possible to measure the Luttinger parameter of the non-chiral liquid formed by the combination of the two counterpropagating edges when we add a small confining potential. While we measure a Luttinger exponent consistent with the chiral Luttinger theory prediction for the full hard-core interaction, the exponent remains non-trivial in the Tao-Thouless limit as well as for simple truncated states that can be constructed on the cylinder. If the radius of the cylinder is taken to infinity the problem becomes a Tonks-Girardeau one-dimensional interacting gas in Fermi and Bose cases. Finally we show that the the Tao-Thouless and truncated states have an edge electron propagator which decays spatially with a Fermi-liquid exponent even if the energy spectrum can still be described by a non-trivial Luttinger parameter.
16 pages, 9 figures
References in corpus (8)
- Fractional Quantum Hall States and Jack Polynomials
- Quantum Hall system in Tao-Thouless limit
- Half-Filled Lowest Landau Level on a Thin Torus
- One-Dimensional Theory of the Quantum Hall System
- Microscopic theory of the quantum Hall hierarchy
- Testing the topological nature of the fractional quantum Hall edge
- Fractional quantum Hall edge: Effect of nonlinear dispersion and edge roton
- Electron operator at the edge of the 1/3 fractional quantum Hall liquid