Manipulating Non-Abelian Anyons in a Chiral Multichannel Kondo Model

Non-Abelian anyons are fractional excitations of gapped topological models believed to describe certain topological superconductors or quantum Hall states. Here, we provide the first numerical evidence that they emerge as independent entities also in gapless electronic models. Starting from a multi-impurity multichannel chiral Kondo model, we introduce a novel mapping to a single-impurity model, amenable to Wilson’s numerical renormalization group. We extract its spectral degeneracy structure and fractional entropy, and calculate the $F$ matrices, which encode the topological information regarding braiding of anyons, directly from impurity spin-spin correlations. Impressive recent advances on realizing multichannel Kondo systems with chiral edges may thus bring anyons into reality sooner than expected.

Figure 1

(a) The impurities are Kondo-coupled to “buffer” dangling sites, which in turn quadratically couple to the chiral channels, and are considered part of the noninteracting bath. (b) Taking the distance between these sites to zero leads to an effective chiral model, in which the dangling sites together with the impurities form a large effective impurity.

Figure 2

Impurity entropy per impurity for two channels (red) with 1–3 impurities, and three channels (blue) with 1–2 impurities, taking $2J=\mathrm{\Gamma }=D/8$. At high temperatures the impurity spins are free, each contributing an entropy of $\log 2$. At low temperatures each impurity contributes a fractional entropy corresponding to the quantum dimension of Ising [$\mathrm{SU}{(2)}_2$] or Fibonacci [$\mathrm{SU}{(2)}_3$] anyons for two or three channels, respectively.

Figure 3

(a) Quantum phase transition for two impurities with two (red) and three (blue) channels as a function of the dangling-site hopping amplitude $t_{12}^{\prime }$, taking $2J=\mathrm{\Gamma }=D/8$. Correlations for the bare singlet and triplet are indicated by dashed lines. (b) Extraction of the $F$ matrix from interimpurity spin correlators in a three-impurity system.