From American University, Prof. Nathan Harshman gave a seminar talk about topological exchange statistics in one spatial dimension on Nov. 17th, 2021. To introduce exchange statistics as done in the literature, he started with statistics for bosons and fermions and extended fractional and non-abelian exchange statistics. Then, the speaker raised questions about particle exchange in 1D and the collisions of the particles. Can a collision and an exchange at all be distinguished in one dimension? Is it reasonable to include points of coincidence in the configuration space? The way to resolve these problems is to introduce orbifolds. After pedagogically explaining the concepts of the orbifolds, he began to use the orbifold topological approach to study exchange statistics for any dimension. This approach offers great chances for novel abelian and nonabelian anyons in effectively 1D cold atom and condensed matter systems.

Reported by Thore Posske (University of Hamburg, Germany) and Ching-Kai Chiu