Nonequilibrium quantum dynamics of the magnetic Anderson model

TL;DR

This paper investigates the non-equilibrium quantum dynamics of a magnetic impurity in a quantum dot, revealing how impurity spin relaxation and Coulomb interactions influence current and spin polarization in a deep quantum regime.

Contribution

The study extends the ISPI method to coupled quantum dot-impurity systems, providing detailed insights into non-equilibrium relaxation processes and impurity effects beyond perturbation theory.

Findings

Impurity spin polarization decays faster with higher bias, temperature, and interaction.

Exact relaxation rates differ from perturbative predictions.

Stationary current decreases with stronger impurity coupling, showing a maximum at finite Coulomb interaction.

Abstract

We study the non-equilibrium dynamics of a spinful single-orbital quantum dot with an incorporated quantum mechanical spin-1/2 magnetic impurity. Due to the spin degeneracy, double occupancy is allowed, and Coulomb interaction together with the exchange coupling of the magnetic impurity influence the dynamics. By extending the iterative summation of real-time path integrals (ISPI) to this coupled system, we monitor the time-dependent non-equilibrium current and the impurity spin polarization to determine features of the time-dependent non-equilibrium dynamics. We particulary focus on the deep quantum regime, where all time and energy scales are of the same order of magnitude and no small parameter is available. We observe a significant influence of the non-equilibrium decay of the impurity spin polarization both in the presence and in the absence of Coulomb interaction. The exponential relaxation is faster for larger bias voltages, electron-impurity interactions and temperatures. We show that the exact relaxation rate deviates from the corresponding perturbative result. In addition, we study in detail the impurity's back action on the charge current and find a reduction of the stationary current for increasing coupling to the impurity. Moreover, our approach allows us to systematically distinguish mean-field Coulomb and impurity effects from the influence of quantum fluctuations and flip-flop scattering, respectively. In fact, we find a local maximum of the current for a finite Coulomb interaction due to the presence of the impurity.