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The Microscopic Picture of Chiral Luttinger Liquid: Composite Fermion Theory of Edge States

Yue Yu·Wenjun Zheng·Zhongyuan Zhu
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Abstract

We derive a microscopic theory of the composite fermions describing the low-lying edge excitations in the fractional quantum Hall liquid. Using the composite fermion transformation, one finds that the edge states of the $ν=1/m$ system in a disc sample are described by, in one dimensional limit, the Calogero-Sutherland model with other interactions between the composite fermions as perturbations. It is shown that a large class of short-range interactions renormalize only the Fermi velocity while the exponent $g=ν=1/m$ is invariant under the condition of chirality. By taking the sharp edge potential into account, we obtain a microscopic justification of the chiral Luttinger liquid model of the fractional quantum Hall edge states. The approach applied to the $ν=1/m$ system can be generalized to the other edge states with odd denominator filling factors.

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Yue Yu, Wenjun Zheng, Zhongyuan Zhu. 1997-09-02. The Microscopic Picture of Chiral Luttinger Liquid: Composite Fermion Theory of Edge States. https://doi.org/10.1103/physrevb.56.13279

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