Band Structure of the Fractional Quantum Hall Effect

TL;DR

This paper explains the origin of energy bands in the fractional quantum Hall effect using composite fermion theory, revealing a microscopic understanding of strongly correlated states akin to Fermi liquid theory.

Contribution

It demonstrates that composite fermion theory provides a complete microscopic description of low-energy bands in the fractional quantum Hall effect.

Findings

Composite fermion theory accurately describes energy bands.

A one-to-one correspondence exists between fractional and integer quantum Hall regimes.

Provides a microscopic understanding of strongly correlated states.

Abstract

The eigenstates of interacting electrons in the fractional quantum Hall phase typically form fairly well defined bands in the energy space. We show that the composite fermion theory gives insight into the origin of these bands and provides an accurate and complete microscopic description of the strongly correlated many-body states in the low-energy bands. Thus, somewhat like in Landau's fermi liquid theory, there is a one-to-one correspondence between the low energy Hilbert space of strongly interacting electrons in the fractinal quantum Hall regime and that of weakly interacting electrons in the integer quantum Hall regime.