Interaction quench dynamics in the Kondo model in presence of a local magnetic field

TL;DR

This paper analyzes the non-equilibrium quench dynamics of the Kondo model with a local magnetic field, revealing that relaxation times are governed by the Kondo scale and oscillations depend on the magnetic field.

Contribution

It provides exact analytical results for the local spin dynamics in the Kondo model with a magnetic field, highlighting the role of finite-size effects in non-equilibrium conditions.

Findings

Relaxation time is set by the Kondo scale.

Damped oscillations occur with frequency proportional to the magnetic field.

Finite-size corrections are crucial in non-equilibrium bosonization.

Abstract

In this work we investigate the quench dynamics in the Kondo model on the Toulouse line in presence of a local magnetic field. It is shown that this setup can be realized by either applying the local magnetic field directly or by preparing the system in a macroscopically spin-polarized initial state. In the latter case, the magnetic field results from a subtlety in applying the bosonization technique where terms that are usually referred to as finite-size corrections become important in the present non-equilibrium setting. The transient dynamics is studied by analyzing exact analytical results for the local spin dynamics. The time scale for the relaxation of the local dynamical quantities turns out to be exclusively determined by the Kondo scale. In the transient regime, one observes damped oscillations in the local correlation functions with a frequency set by the magnetic field.