Frractional Chern Insulators
Résumé
The interest in the field of topological insulators has exploded in recent years. Topological insulators are mainly one body problems, neglecting interactions. As such, the type of interacting topologically ordered state with fractional statistic quasiparticles such as the fractional quantum Hall (FQH) has not been found or proposed in an weakly interact ing topological insulator. We will show that recent numerical studies, based on exact diagonalizations, convincingly indicates that FQH phases may emerge in strongly interacting topological insulators. We will see that the fractional Chern insulators might also lead to phases that are different from those one can find in usual FQH systems.