Explicit mapping between a 2D quantum Hall system and a 1D Luttinger liquid, I. Luttinger parameters
arXiv:cond-mat/0701322 · doi:10.1103/PhysRevB.76.195321
Abstract
We study a simple model of a quantum Hall system with the electrons confined to a linear, narrow channel. The system is mapped to a 1D system which in the low-energy approximation has the form of a Luttinger liquid with different interactions between particles of equal and of opposite chiralities. We study this mapping at the microscopic level, and discuss the relation between the parameters of the 2D system and the corresponding 1D Luttinger liquid parameters. We focus in particular on how the parameters are renormalized by the electron interactions and show that the velocity parameter of the current is not modified by the interaction.
Latex, 22 pages, 1 figure
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- From fractional boundary charges to quantized Hall conductance
- Are there sharp fractional charges in Luttinger liquids?
- Charge Fractionalization on Quantum Hall Edges
- Explicit mapping between a 2D quantum Hall system and a 1D Luttinger liquid. II. Correlation functions
- Quasi-particle propagation in quantum Hall systems
- Gauge-Invariant Variables Reveal the Quantum Geometry of Fractional Quantum Hall States
- Luttinger liquids, Fermi liquids and fractional statistics