Unveiling the internal entanglement structure of the Kondo singlet

Abstract: We disentangle all the individual degrees of freedom in the quantum impurity problem to deconstruct the Kondo singlet, both in real and energy space, by studying the contribution of each individual free electron eigenstate. This is a problem of two spins coupled to a bath, where the bath is formed by the remaining conduction electrons. Being a mixed state, we resort to the "concurrence" to quantify entanglement. We identify "projected natural orbitals" that allow us to individualize a single-particle electronic wave function that is responsible of more than $90\%$ of the impurity screening. In the weak coupling regime, the impurity is entangled to an electron at the Fermi level, while in the strong coupling regime, the impurity counterintuitively entangles mostly with the high energy electrons and disentangles completely from the low-energy states carving a "hole" around the Fermi level. This enables one to use concurrence as a pseudo order parameter to compute the characteristic "size" of the Kondo cloud, beyond which electrons are are weakly correlated to the impurity and are dominated by the physics of the boundary.