Speaker
Description
Non-Abelian anyons typically emerge in gapped topological models, and give rise to a fusion space which scales with a fractional quantum dimension to the power of the number of anyons. It is also well established that a single spin-1/2 impurity coupled to $k$ multiple fermionic channels results in a fractional entropy equal to the quantum dimension of a single $SU(2)_k$ anyon. Generalizing this to multiple impurities, thus giving rise to an anyonic fusion space in a gapless electronic model, has long been a challenge. Employing Wilson’s numerical renormalization group (NRG) we demonstrate that by utilizing chiral channels (e.g., integer quantum Hall edge states), this is possible. First we introduce a chiral generalization of NRG [PRB 107, 155417], and prove that due to chirality, locally the physics is indifferent to the inter-impurity distance. Armed with this insight, we map a multi-impurity chiral model to an effective single-impurity model [PRL 129, 227703], amenable to standard NRG, and demonstrate the emergence of an anyon at each impurity. We further demonstrate that the anyonic fusion space can be manipulated, i.e., braided, by measurements of inter-impurity spin correlations. Impressive recent advances on realizing multichannel Kondo systems with chiral edges may thus bring non-Abelian anyons into existence in the near future.
