On the stability of Laughlin's fractional quantum Hall phase

Contribution to the second edition of the Encyclopedia of condensed matter physics. Partially based on two previous review texts by the same author.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