Universal entanglement of the multi-channel Kondo effects

An essential concept of the impurity problem is the quantum coherent screening of the impurity. In this work, we develop a method to compute the entanglement negativity between the impurity and its environment in spin-1/2 impurity problems, based on the boundary conformal field theory. We apply our method to the multichannel Kondo model, a strongly correlated system in which conduction electrons of multiple channels compete to screen one impurity, to unveil quantum coherence inside the Kondo screening length. We show that the entanglement has the maximal value independent of the number of the screening channels at zero temperature. At low temperature, we show that the entanglement exhibits a power-law thermal decay with a fractional number exponent, and it is attributed to the boundary conformal primary field representing the impurity. These results are confirmed by the numerical renormalization group. We quantify the spatial distribution of the Kondo screening cloud through the entanglement. Using the quantification, we suggest how to detect the multichannel Kondo cloud in a quantum dot device.