Explicit mapping between a 2D quantum Hall system and a 1D Luttinger liquid, I. Luttinger parameters

Details Explicit mapping between a 2D quantum Hall system and a 1D Luttinger liquid, I. Luttinger parameters Explicit mapping between a 2D quantum Hall system and a 1D Luttinger liquid, I. Luttinger parameters

2007-01-15

arxiv.org/abs/cond-mat/0701322v1

Phys. Rev. B 76, 195321 (2007)

Physics

Condensed Matter

Strongly Correlated Electrons

Latex, 22 pages, 1 figure

Scientific paper

10.1103/PhysRevB.76.195321

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.

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