Correlations in Fractional Hall Effect

Abstract

Although most of the experimental facts^1–4 about the fractional quantum Hall effect can be understood on the basis of Laughlin wave function⁵ or its generalizations^6–10, there still remains questions connected with the correlations and the thermodynamic limit. Many calculations have been done for few electron systems^11–13. They are all restricted to the lowest Landau level, the argument also used by Laughlin⁵ to set up his function. Can this restriction be relaxed? With a notable exception¹⁵ most of the calculations in the thermodynamic limit use the analogy with the classical one-component plasma^5,16–18 to show e.g. that the Laughlin state lies lower in energy than the CDW (Charge-Density Wave)-states. The connection between a classical system and a physically completely different system is always interesting, but the restriction to only two particle correlations usually sets the limit to the practical usefulness of the analogy.