Long-time relaxation dynamics of a spin coupled to a Chern insulator

TL;DR

This study investigates the long-time relaxation behavior of a classical spin coupled to the edge of a one-dimensional topological insulator model, revealing how topological states influence spin dynamics and relaxation processes.

Contribution

It provides a numerical analysis of spin relaxation in a topological insulator model, highlighting the effects of edge states and topological phases on relaxation dynamics.

Findings

Topological edge states significantly affect spin relaxation.

Dynamical phase diagrams distinguish trivial and nontrivial phases.

Retardation effects are crucial for understanding long-time relaxation.

Abstract

The relaxation of a classical spin, exchange coupled to the local magnetic moment at an edge site of the one-dimensional spinful Su-Schrieffer-Heeger model is studied numerically by solving the full set of equations of motion. A Lindblad coupling of a few sites at the opposite edge to an absorbing bath ensures that convergence with respect to the system size is achieved with only a moderate number of core sites. This allows us to numerically exactly study the long-time limit and to determine the parameter regimes where spin relaxation takes place. Corresponding dynamical phase diagrams for the topologically trivial and the nontrivial cases are constructed. The dynamical phase boundaries, the role of the topological edge state and its internal Zeeman splitting for the spin-relaxation process, as well as incomplete spin relaxation on long time scales can be explained within the framework of a renormalized linear-response approach when explicitly taking retardation effects and nonequilibrium spin-exchange processes into account.