Edge properties of principal fractional quantum Hall states in the cylinder geometry

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.

arXiv comment16 pages, 9 figures

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• Probing the geometry of the Laughlin state
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• Numerical investigation of gapped edge states in fractional quantum Hall-superconductor heterostructures
• Braiding fractional quantum Hall quasiholes on a superconducting quantum processor
• Bubble phase at $\nu =1/3$ for a spinless hollow-core interaction
• Vortex and fractional quantum Hall phases in a rotating anisotropic Bose gas
• Quantum Hall correlations in tilted extended Bose-Hubbard chains