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Springer series in solid-state sciences

Narrow-Channel Fractional Quantum Hall States and Their Projection into One Dimension — Non-Tomonaga-Luttinger-Liquid Behavior

D. Yoshioka, Masao Ogata

Published Jan 1, 1994• 0 citations
Publisher
DOI
10.1007/978-3-642-85129-2_17

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Abstract Tomonaga–Luttinger liquids exhibit unique features that cannot be seen in ordinary Fermi liquids. Recent advancement in measurement techniques on 1D quantum Hall edge channels allows to reveal unique characteristics, such as spin‐charge separation and nonthermal metastable states. In this review, an overview of nonequilibrium dynamics in quantum‐Hall Tomonaga–Luttinger liquids is presented. After the introduction of a circuit model for collective excitations (bosons) in the system, transport eigenmodes in interaction‐ and disorder‐dominated regimes are discussed with time‐resolved charge measurements for the integer and fractional quantum Hall systems. Moreover, nonthermal steady states associated with the integrable model are studied with energy distribution functions obtained with a quantum dot spectrometer. These nontrivial dynamics can be extended to other 1D systems, including 2D topological insulators.
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We study the universal long distance behavior of the Laughlin state for the fractional quantum Hall effect and the ground state of the Calogero-Sutherland model (one-dimensional 1/r2 interaction model). In particular, it is shown that these two wave functions coincide exactly when Laughlin state is confined in a narrow cylinder geometry. The seeming difference of dimensionality is merely a difference of representation of wave functions. We also give a recipe to interpret operators acting on states in the lowest Landau level in terms of the usual one-dimensional fermion operators, which is important for extracting the Tomonaga-Luttinger liquid behavior of the edge states.