Relaxation vs decoherence: Spin and current dynamics in the anisotropic Kondo model at finite bias and magnetic field

TL;DR

This paper investigates the real-time spin and current dynamics in the anisotropic Kondo model under finite bias and magnetic field using a nonequilibrium renormalization group approach, revealing decay rates and universal short-time behavior.

Contribution

It provides analytic expressions for the time evolution of spin and current in the weak-coupling regime, including decay rates and the identification of low-energy cutoffs for logarithmic terms.

Findings

All observables decay with spin relaxation and decoherence rates.

Various V-dependent logarithmic, oscillatory, and power-law contributions are identified.

Universal dynamics are observed for small times t << 1/max{V,h0}.

Abstract

Using a nonequilibrium renormalization group method we study the real-time evolution of spin and current in the anisotropic Kondo model (both antiferromagnetic and ferromagnetic) at finite magnetic field $h_0$ and bias voltage $V$. We derive analytic expressions for all times in the weak-coupling regime $\max\{V,h_0,1/t\}\gg T_c$ ($T_c=$ strong coupling scale). We find that all observables decay both with the spin relaxation and decoherence rates $\Gamma_{1/2}$. Various $V$-dependent logarithmic, oscillatory, and power-law contributions are predicted. The low-energy cutoff of logarithmic terms is generically identified by the difference of transport decay rates. For small times $t\ll \max\{V,h_0\}^{-1}$, we obtain universal dynamics for spin and current.