Spin Precession and Real Time Dynamics in the Kondo Model: A Time-Dependent Numerical Renormalization-Group Study

Abstract

A detailed derivation of the recently proposed time-dependent numerical renormalization-group (TD-NRG) approach to nonequilibrium dynamics in quantum impurity systems is presented. We demonstrate that the method is suitable for fermionic as well as bosonic baths. A comparison with exact analytical results for the charge relaxation in the resonant-level model and for dephasing in the spin-boson model establishes the accuracy of the method. The real-time dynamics of a single spin coupled to both types of baths is investigated. We use the TD-NRG to calculate the spin relaxation and spin precession of a single Kondo impurity. The short- and long-time dynamics is studied as a function of temperature in the ferromagnetic and antiferromagnetic regimes. The short-time dynamics agrees very well with analytical results obtained at second order in the exchange coupling $J$. In the ferromagnetic regime, the long-time spin decay is described by the scaling variable $x=2{\rho }_{F}J(T)Tt$. In the antiferromagnetic regime it is governed for $T<T_K$ by the Kondo time scale $1/T_K$. Here ${\rho }_F$ is the conduction-electron density of states and $T_K$ is the Kondo temperature. Results for spin precession are obtained by rotating the external magnetic field from the x axis to the z axis.

Revtex, 21 pages, 11 figures, 1 table

References in corpus (6)

• Real time evolution using the density matrix renormalization group
• Real-time dynamics in Quantum Impurity Systems: A Time-dependent Numerical Renormalization Group Approach
• Numerical Renormalization Group for Bosonic Systems and Application to the Subohmic Spin-Boson Model
• A Numerical Renormalization Group approach to Green's Functions for Quantum Impurity Models
• Comment on "Time-Dependent Density-Matrix Renormalization Group: A Systematic Method for the Study of Quantum Many-Body Out-of- Equilibrium Systems"
• Electron Transfer in Donor-Acceptor Systems: Many-Particle Effects and Influence of Electronic Correlations

Cited by in corpus (23)

• The numerical renormalization group method for quantum impurity systems
• Sum-rule Conserving Spectral Functions from the Numerical Renormalization Group
• Diagrammatic Monte Carlo simulation of non-equilibrium systems
• A Numerical Renormalization Group approach to Green's Functions for Quantum Impurity Models
• On steady-state currents through nano-devices: a scattering-states numerical renormalization group approach to open quantum systems
• Iterative real-time path integral approach to nonequilibrium quantum transport
• Real-time simulations of nonequilibrium transport in the single-impurity Anderson model
• Equilibrium and non-equilibrium dynamics of the sub-ohmic spin-boson model
• Full counting statistics for noninteracting fermions: Exact results and the Levitov-Lesovik formula
• Transport properties and Kondo correlations in nanostructures: the time-dependent DMRG method applied to quantum dots coupled to Wilson chains
• Zero-bias conductance in carbon nanotube quantum dots
• Real Time Evolution in Quantum Many-Body Systems With Unitary Perturbation Theory
• Matrix product state comparison of the numerical renormalization group and the variational formulation of the density matrix renormalization group
• A Numerical Renormalization Group approach to Non-Equilibrium Green's Functions for Quantum Impurity Models
• Kondo physics and dissipation: A numerical renormalization-group approach to Bose-Fermi Kondo models
• Unitary perturbation theory approach to real-time evolution problems
• Influence of disorder on the transport properties of heavy-fermion systems
• Dissipative Two-Electron Transfer
• Quantum phase transitions in the extended periodic Anderson model
• Kondo resonance in an ac driven quantum dot subjected to finite bias
• Magnetic properties of the extended periodic Anderson model
• Dynamics of large anisotropic spin in a sub-ohmic dissipative environment close to a quantum-phase transition
• Decoherence and relaxation in the interacting quantum dot system