From Composite Fermions to Calogero-Sutherland Model: Edge of Fractional Quantum Hall Liquid and the Dimension Reduction

Abstract

We derive a microscopic model describing the low-lying edge excitations in the fractional quantum Hall liquid with $\nu =\frac{{\nu }^{\ast }}{\tilde{\varphi }{\nu }^{\ast }+1}$. For ${\nu }^{\ast }>0$, it is found that the composite fermion model reduces to an SU$({\nu }^{\ast })$ Calogero-Sutherland model in a dimension reduction, whereas it is not exact soluble for ${\nu }^{\ast }<0$. However, the ground states in both cases can be found and the low-lying excitations can be shown the chiral Luttinger liquid behaviors. On the other hand, we shows that the finite temperature behavior of $G-T$ curve will deviate from the prediction of the chiral Luttinger liquid. We also point out that the suppression of the `spin' degrees of freedom agrees with very recent experiments by Chang et al. The two-boson model of Lee and Wen is described microscopically.

4 pages, Revtex, accepted for publication by PRB

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• Towards a field theory of the fractional quantum Hall states
• A dipole interpretation of the $\nu =1/2$ state
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Cited by in corpus (4)

• Fractional exclusion statistics and shot noise in ballistic conductors
• Dynamics of edge Majorana fermions in $\nu =\frac{5}{2}$ fractional quantum Hall effects
• The length scale measurements of the Fractional quantum Hall state on cylinder
• Fractionally charged anyon generated by topological path fusion in magnetic flux lattice