Thanks! But this review seems just focus on anyons, right?atyy said:I read about the first third of Ady Stern's intrduction, and it seemed quite friendly.
http://arxiv.org/abs/0711.4697
A fractional quantum hall effect (FQHE) is a phenomenon that occurs in 2D electron systems at low temperatures and high magnetic fields. It describes the fractional quantization of the Hall conductance, which is the ratio of the induced voltage to the applied current in the presence of a magnetic field.
The FQHE is important because it provides evidence for the existence of fractional charges in nature, which was previously only theorized. It also allows for the study of highly correlated electrons and topological phases of matter.
The FQHE is caused by the strong interactions between electrons in a 2D system, which leads to the formation of a collective state called the electron liquid. This liquid has unique properties, such as the fractional quantization of the Hall conductance, that are not observed in non-interacting systems.
Landau levels are discrete energy levels that electrons can occupy in a 2D system in the presence of a magnetic field. In the FQHE, the interactions between electrons cause these levels to split into smaller sub-levels, leading to the fractional quantization of the Hall conductance.
The FQHE has potential applications in quantum computing, as the fractional charges and topological phases of matter could be used to store and manipulate information. It also has implications in fields such as materials science and condensed matter physics.