On the stability of Laughlin's fractional quantum Hall phase

TL;DR

This paper reviews Laughlin's 1983 theory of the fractional quantum Hall effect, emphasizing the mathematical physics perspective and explaining the rigidity and incompressibility of Laughlin's states as key to understanding the phenomenon.

Contribution

It provides a detailed mathematical physics analysis of Laughlin's ground and excited states, clarifying their rigidity and incompressibility properties.

Findings

Laughlin states are rigid and incompressible liquids

The rigidity explains the quantized Hall resistance

Mathematical physics perspective clarifies the effect's origin

Abstract

The fractional quantum Hall effect in 2D electron gases submitted to large magnetic fields remains one of the most striking phenomena in condensed matter physics. Historically, the first observed signature is a Hall resistance quantized to the value (2m+1) when the filling factor (electron density divided by magnetic flux quantum density) of a 2D electron gas is in the vicinity of an inverse odd integer 1/(2m +1). This was one of the first observation of fractional quantum numbers. A large part of our basic theoretical understanding of this effect (and descendants) originates from Laughlin's theory of 1983, reviewed here from a mathematical physics perspective. We explain in which sense Laughlin's proposed ground and excited states for the system are rigid/incompressible liquids, and why this is crucial for the explanation of the effect.