Accessing long timescales in the relaxation dynamics of spins coupled to a conduction-electron system using absorbing boundary conditions

Abstract

The relaxation time of a classical spin interacting with a large conduction-electron system is computed for a weak magnetic field, which initially drives the spin out of equilibrium. We trace the spin and the conduction-electron dynamics on a time scale, which exceeds the characteristic electronic scale that is set by the inverse nearest-neighbor hopping by more than five orders of magnitude. This is achieved with a novel construction of absorbing boundary conditions, which employs a generalized Lindblad master-equation approach to couple the edge sites of the conduction-electron tight-binding model to an external bath. The failure of the standard Lindblad approach to absorbing boundaries is traced back to artificial excitations initially generated due to the coupling to the bath. This can be cured by introducing Lindblad parameter matrices and by fixing those matrices to perfectly suppress initial-state artifacts as well as reflections of physical excitations propagating to the system boundaries. Numerical results are presented and discussed for generic one-dimensional models of the electronic structure.

12 pages, 9 figures, v2 with minor modifications

References in corpus (4)

• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Microscopic approach to current-driven domain wall dynamics
• Nonequilibrium Dynamical Mean Field Theory: an auxiliary Quantum Master Equation approach
• Super-fermion representation of the Lindblad master equation for the electron transport problem

Cited by in corpus (10)

• When can localized spins interacting with conduction electrons in ferro- or antiferromagnets be described classically via the Landau-Lifshitz equation: Transition from quantum many-body entangled to quantum-classical nonequilibrium states
• Long-time relaxation dynamics of a spin coupled to a Chern insulator
• Electron-mediated entanglement of two distant macroscopic ferromagnets within a nonequilibrium spintronic device
• Emergent Non-Abelian Gauge Theory in Coupled Spin-Electron Dynamics
• Dynamics of spin relaxation in nonequilibrium magnetic nanojunctions
• Nonequilibrium dynamics in a spin valve with noncollinear magnetization
• Controlling the real-time dynamics of a spin coupled to the helical edge states of the Kane-Mele model
• Microscopic theory of spin friction and dissipative spin dynamics
• Prerelaxation in quantum, classical, and quantum-classical two-impurity models
• Spin transport through a nanojunction with a precessing anisotropic molecular spin: Quantum interference and spin-transfer torque