Kareljan Schoutens
Non-abelian anyons in 2+1 dimensions
Quantum physics in 2+1 dimensions allows for the spectacular possibility of non-Abelian braid statistics. It arises when a topological quantum material is such that a small number of excitations, at fixed position, give rise to a degenerate space of states, and when the braiding of such excitations is represented as a matrix acting on the state vector. The patterns of fusion and braiding of excitations (`anyons¹) in bosonic 2D systems with non-Abelian statistics are captured by the mathematical notion of a modular tensor category (MTC). We present recent results, obtained with X.-G. Wen, on the classification and construction of MTC¹s with a limited number (up to N=6) of anyon-types.