THE CHERN–SIMONS–LANDAU–GINZBURG THEORY OF THE FRACTIONAL QUANTUM HALL EFFECT

Abstract

This paper gives a systematic review of a field theoretical approach to the fractional quantum Hall effect (FQHE) that has been developed in the past few years. We first illustrate some simple physical ideas to motivate such an approach and then present a systematic derivation of the Chern–Simons–Landau–Ginzburg (CSLG) action for the FQHE, starting from the microscopic Hamiltonian. It is demonstrated that all the phenomenological aspects of the FQHE can be derived from the mean field solution and the small fluctuations of the CSLG action. Although this formalism is logically independent of Laughlin's wave function approach, their physical consequences are equivalent. The CSLG theory demonstrates a deep connection between the phenomena of superfluidity and the FQHE, and can provide a simple and direct formalism to address many new macroscopic phenomena of the FQHE.