Non-Abelian Kondo Anyons - Multiple Quantum Impurities Coupled to Multiple Chiral Edge Modes

Non-abelian anyons are fractional excitations of gapped topological models believed to describe certain topological superconductors or quantum Hall states. We provide numerical evidence that they emerge as independent entities also in gapless electronic models. It is well established that coupling a single spin-1/2 impurity to k multiple fermionic channels leads to frustration and fractionalization of the impurity degrees of freedom, resulting in a fractional entropy equal to the quantum dimension of a single SU(2)_k anyon. It has recently been conjectured that by utilizing chiral channels (e.g., integer quantum Hall edge states) this could be generalized to multiple impurities, leading to a decoupled non-abelian SU(2)_k fusion space with an anyon for each impurity [1,2].

Developing a chiral generalization of Wilson's numerical renormalization group (NRG), we show that local quantities of impurities coupled to chiral channels are indifferent to the inter-impurity distance [3], and armed with this insight, we introduce a novel mapping of a multi-impurity chiral model to an effective single-impurity model [4], amenable to standard NRG. With this we demonstrate the emergence of the conjectured non-abelian fusion space, and show it can be manipulated by measuring inter-impurity spin correlations. Impressive recent advances on realizing multichannel Kondo systems with chiral edges [5,6] may thus bring non-abelian anyons into existence in the near future.