Nonequilibrium, spatio-temporal formation of the Kondo screening-cloud on a lattice

TL;DR

This paper investigates the real-time formation of the Kondo screening cloud after a quantum quench, revealing emergent spatiotemporal scales, a light cone at Fermi velocity, and power-law decay outside the cone, using advanced numerical methods.

Contribution

It provides a detailed nonequilibrium analysis of Kondo cloud formation on a lattice, identifying distinct time scales and dynamic energy scales related to the Kondo temperature.

Findings

Emergent length and time scales in correlation functions.

Identification of a light cone moving at the Fermi velocity.

Power-law decay of correlations outside the light cone.

Abstract

We study the nonequilibrium formation of a spin screening cloud that accompanies the quenching of a local magnetic moment immersed in a Fermi sea at zero temperature. Based on high precision density matrix renormalization group results for the interacting single impurity Anderson model we discuss the real time evolution after a quantum quench in the impurity-reservoir hybridization using time evolving block decimation. We report emergent length and time scales in the spatiotemporal structure of non-local correlation functions in the spin- and the charge density channel. At equilibrium, our data for the correlation functions and the extracted length-scales show good agreement with existing results, as do local time dependent observables at the impurity. In the time-dependent data, we identify a major signal which defines a "light cone" moving at the Fermi velocity and a ferromagnetic component in its wake. Inside the light cone we find that the structure of the nonequilibrium correlation functions emerges on two time scales. Initially, the qualitative structure of the correlation functions develops rapidly at the lattice Fermi velocity. Subsequently the spin correlations converge to the equilibrium results on a much larger time scale. This process sets a dynamic energy scale, which we identify to be proportional to the Kondo temperature. Outside the light cone we observe two different power law decays of the correlation functions in space, with time and interaction strength independent exponents.