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arXiv · 1207.3267

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

Paul Soulé·Thierry Jolicoeur
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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.

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Paul Soulé, Thierry Jolicoeur. 2012-07-13. Edge properties of principal fractional quantum Hall states in the cylinder geometry. https://doi.org/10.1103/physrevb.86.115214

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