Nonequilibrium Spin Dynamics in the Ferromagnetic Kondo Model

Abstract

Motivated by recent experiments on molecular quantum dots we investigate the relaxation of pure spin states when coupled to metallic leads. Under suitable conditions these systems are well described by a ferromagnetic Kondo model. Using two recently developed theoretical approaches, the time-dependent numerical renormalization group and an extended flow equation method, we calculate the real-time evolution of a Kondo spin into its partially screened steady state. We obtain exact analytical results which agree well with numerical implementations of both methods. Analytical expressions for the steady state magnetization and the dependence of the long-time relaxation on microscopic parameters are established. We find the long-time relaxation process to be much faster in the regime of anisotropic Kondo couplings. The steady state magnetization is found to deviate significantly from its thermal equilibrium value.

Short-time universal scaling in an isolated quantum system after a quench

“…[70,71]), and for quantum impurities (see, e.g., Refs. [53,54]). At one loop and for times larger than the microscopic time Λ −1 (before which the dynamics is non-universal), the resulting RG equations read (see Appendix A)…”

“…This is known to occur for quenches in * These authors contributed equally. classical systems in the presence of a thermal bath [49][50][51][52] and, more recently, for quantum impurities [53,54] or open quantum systems [55,56]. A quench introduces a "temporal boundary" by breaking the time-translational invariance (TTI) that characterizes equilibrium dynamics, causing the emergence of short-time universal scaling, analogous to universal short-distance scaling in the presence of spatial boundaries in equilibrium [57][58][59].…”

Decoherence and lead-induced interdot coupling in nonequilibrium electron transport through interacting quantum dots: A hierarchical quantum master equation approach

“…74 Numerically exact schemes based on time-convolutionless master equations, 75 numerical [76][77][78] and functional 33,79 renormalization group theory, 35 density matrix renormalization group methods, [80][81][82] flow equation approaches, [83][84][85] iterative [86][87][88] and stochastic [89][90][91][92][93] diagrammatic methods, and wave-function propagation algorithms 94,95 have also been used. Additionally, numerically exact reduced dynamics techniques, which exist for population dynamics 96 and transport properties, 97 have been applied to both the stochastic diagrammatic methods 98 and the wave-function propagation schemes.…”

Quench dynamics of correlated quantum dots

“…Several many-body methods successfully used in equilibrium were recently extended, allowing one to study the dynamics of correlated quantum dots out of nonequilibrium states; some of those are (mainly) analytical 4-7 while others are purely numerical. 4,[8][9][10][11][12] Only a few of these techniques have been used to treat Hamiltonians with explicitly time dependent parameters. We apply a recently developed approximate semianalytical method 13 which is based on an extension of the functional renormalization group (RG) approach 14 to Keldysh Green functions.…”