Spatiotemporal buildup of the Kondo screening cloud

TL;DR

This paper analytically studies the dynamic formation of the Kondo screening cloud in space and time, revealing a light cone effect and power-law tails outside the cone at zero temperature.

Contribution

It provides exact analytical results at the Toulouse point for the spatiotemporal buildup of the Kondo screening cloud after switching on the coupling.

Findings

Light cone in spin susceptibility due to causality

Power-law decay of correlations outside the light cone at T=0

Initial entanglement causes tails in correlation functions

Abstract

We investigate how the Kondo screening cloud builds up as a function of space and time. Starting from an impurity spin decoupled from the conduction band, the Kondo coupling is switched on at time t=0. We work at the Toulouse point where one can obtain exact analytical results for the ensuing spin dynamics at both zero and nonzero temperature T. For t>0 the Kondo screening cloud starts building up in the wake of the impurity spin being transported to infinity. In this buildup process the impurity spin--conduction band spin susceptibility shows a sharp light cone due to causality, while the corresponding correlation function has a tail outside the light cone. At T=0 this tail has a power law decay as a function of distance from the impurity, which we interpret as due to initial entanglement in the Fermi sea.