Speaker
Nicolas Rougerie, ENS Lyon
Abstract
Anyon braiding statistics were first introduced by Leinaas and Myrheim as a funny theoretical possibility: in a 2D world, quantum particles need not, from first principles, be either bosons or fermions. The exchange phase could be ANY number. Next emerged the idea that anyons could be realized as quasi-particles, in particular in the fractional quantum Hall effect setting. A major argument by Arovas-Schrieffer-Wilczek used a Berry phase calculation to suggest this, hence for ever after relating “anyonic quantum particles” with “excitations of a quantum system carrying exotic Berry phases upon braiding”.
I will try to review how and why the two notions are related or differ, and outline some elements about where we stand mathematically on the question.