Scaling approach for the time-dependent Kondo model

TL;DR

This paper introduces a nonperturbative scaling method for the time-dependent Kondo model, enabling analysis of impurity spin dynamics during switching processes, bridging quenched and adiabatic regimes.

Contribution

It extends Wegner's flow equations to time-dependent Hamiltonians, providing a novel approach to analyze quantum many-body systems with time-dependent interactions.

Findings

Impurity spin expectation value interpolates between quenched and adiabatic limits.

The method offers a continuous description of spin dynamics during switching.

Applicable to models with time-dependent interactions in quantum impurity systems.

Abstract

We present a new nonperturbative method to deal with the time-dependent quantum many-body problem, which is an extension of Wegner's flow equations to time-dependent Hamiltonians. The formalism provides a scaling procedure for the set of time-dependent interaction constants. We apply these ideas to a Kondo model with a ferromagnetic exchange coupling switched on over a time scale $\tau$. We show that the asymptotic expectation value of the impurity spin interpolates continuously between its quenched and adiabatic value.