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

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.

12 pages, 11 figures, v2 with minor corrections, as published

References in corpus (7)

• Reading and Writing Single-Atom Magnets
• Spin Inelastic Electron Tunneling Spectroscopy on Local Spin Adsorbed on Surface
• Excitation of local magnetic moments by tunnelling electrons
• Semiclassical dynamics of spin density waves
• Accessing long timescales in the relaxation dynamics of spins coupled to a conduction-electron system using absorbing boundary conditions
• Single atom anisotropic magnetoresistance on a topological insulator surface
• Spin dynamics of $3d$ and $4d$ impurities embedded in prototypical topological insulators

Cited by in corpus (7)

• Emergent Non-Abelian Gauge Theory in Coupled Spin-Electron Dynamics
• Dynamical relaxation behavior of extended XY chain with gapless phase following a quantum quench
• Exchangeless braiding of Majorana zero modes in weakly coupled Kitaev chains
• Prerelaxation in quantum, classical, and quantum-classical two-impurity models
• Microscopic theory of spin friction and dissipative spin dynamics
• Relaxation dynamics in the alternating XY chain following a quantum quench
• Relaxation dynamics of a quantum spin coupled to a topological edge state