The last word in strong correlations

TL;DR

This paper reviews the Hamiltonian Theory of the Fractional Quantum Hall Effect, focusing on the strongly correlated limit where kinetic energy is negligible and interactions dominate, providing insights into the complex many-body problem.

Contribution

It offers a concise review of the Hamiltonian approach to FQHE, emphasizing the strongly correlated limit and the role of interactions in lifting degeneracy.

Findings

Hamiltonian Theory effectively describes FQHE in the strong correlation limit

Interactions lift degeneracy and mix higher Landau levels

Provides a framework for understanding the most strongly correlated regime

Abstract

In the Fractional Quantum Hall Effect (FQHE), in the noninteracting limit, only a fraction $\nu $ of the Lowest Landau Level (LLL) is occupied, producing a huge degeneracy. Interactions lift this degeneracy and mix in higher LL's. In the limit in which we ignore all but the LLL (i.e., let the inverse electron mass ${1 \over m}\to \infty$), the kinetic energy is an irrelevant constant and the ratio of potential to kinetic energy is essentially infinite, making this the most strongly correlated problem imaginable. I give a telegraphic review of the Hamiltonian Theory of the FQHE developed with Ganpathy Murthy that deals with this problem with some success. A nodding acquaintance with FQHE physics is presumed.