Inertia effects in the real-time dynamics of a quantum spin coupled to a Fermi sea

TL;DR

This paper investigates the real-time dynamics of a quantum spin in a Kondo impurity model, revealing quantum-specific effects like rapid nutation damping, and compares quantum and classical spin behaviors.

Contribution

It demonstrates quantum effects such as nutation and its rapid damping in spin dynamics, providing a detailed comparison with classical models and explaining the damping via quantum dephasing.

Findings

Quantum nutation is observed in spin dynamics.

Nutation damping occurs on an extremely short timescale.

Qualitative agreement exists between quantum and classical dynamics for S=1/2.

Abstract

Spin dynamics in the Kondo impurity model, initiated by suddenly switching the direction of a local magnetic field, is studied by means of the time-dependent density-matrix renormalization group. Quantum effects are identified by systematic computations for different spin quantum numbers $S$ and by comparing with tight-binding spin-dynamics theory for the classical-spin Kondo model. We demonstrate that, besides the conventional precessional motion and relaxation, the quantum-spin dynamics shows nutation, similar to a spinning top. Opposed to semiclassical theory, however, the nutation is efficiently damped on an extremely short time scale. The effect is explained in the large-$S$ limit as quantum dephasing of the eigenmodes in an emergent two-spin model that is weakly entangled with the bulk of the system. We argue that, apart from the Kondo effect, the damping of nutational motion is essentially the only characteristics of the quantum nature of the spin. Qualitative agreement between quantum and semiclassical spin dynamics is found down to $S=1/2$.