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

TL;DR

This paper investigates fractional quantum Hall states in cylinder geometry, analyzing edge properties, Luttinger parameters, and the effects of geometry and truncation on edge excitations and correlations.

Contribution

It demonstrates how to measure Luttinger parameters in cylinder geometry and explores edge behavior in various limits, including Tao-Thouless and infinite radius.

Findings

Measured Luttinger exponents consistent with chiral Luttinger theory.

Edge electron propagator decays with Fermi-liquid exponent despite non-trivial Luttinger parameters.

Edge properties vary with cylinder radius and state truncation, revealing complex edge physics.

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.