Multi-impurity chiral Kondo model: correlation functions and anyon fusion rules

TL;DR

This paper investigates the correlation functions in the multichannel chiral Kondo model, revealing how impurity-spin correlations reflect anyon fusion channels, with implications for topological quantum computing.

Contribution

It demonstrates that impurity-spin correlations in the multichannel chiral Kondo model can probe anyon fusion channels, combining conformal field theory and exactly solvable models.

Findings

Impurity-spin correlations depend on anyon fusion channels.

Correlation functions can be used to braid Kondo anyons.

The study connects impurity correlations with topological quantum computing.

Abstract

The multichannel Kondo model supports effective anyons on the partially screened impurity, as suggested by its fractional impurity entropy. It was recently demonstrated for the multi-impurity chiral Kondo model, that scattering of an electron through the impurities depends on the anyon's total fusion channel. Here we study the correlation between impurity-spins. We argue, based on a combination of conformal field theory, a perturbative limit with a large number of channels $k$, and the exactly solvable two-channel case, that the inter-impurity spin correlation probes the anyon fusion of the pair of correlated impurities. This may allow, using measurement-only topological quantum computing protocols, to braid the multichannel Kondo anyons via consecutive measurements.