Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
1997-09-02
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
revtex, 12 pages, no figures, to be published in PRB
Scientific paper
10.1103/PhysRevB.56.13279
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 $\nu=1/m$ 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 $g=\nu=1/m$ 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 $\nu=1/m$ system can be generalized to the other edge states with odd denominator filling factors.
Yu Yue
Zheng Wenjun
Zhu Zhongyuan
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