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

TL;DR

This paper introduces a novel Lindblad-based absorbing boundary condition method that enables simulation of spin relaxation dynamics over extremely long timescales in conduction-electron systems, surpassing previous limitations.

Contribution

The authors develop a generalized Lindblad approach with parameter matrices to effectively absorb excitations and extend the simulation timescale for spin-electron relaxation dynamics.

Findings

Successfully simulated relaxation over five orders of magnitude longer than electronic timescales.

Identified and mitigated artifacts caused by initial bath coupling.

Demonstrated effectiveness on one-dimensional electronic models.

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.