Spatial and temporal propagation of Kondo correlations

Abstract

We address the fundamental question how the spatial Kondo correlations are building up in time assuming an initially decoupled impurity spin ${\vec{S}}_{\mathrm{imp}}$. We investigate the time-dependent spin-correlation function $\chi (\vec{r},t)=⟨{\vec{S}}_{\mathrm{imp}}\vec{s}(\vec{r})⟩(t)$ in the Kondo model with antiferromagnetic and ferromagnetic couplings where $\vec{s}(\vec{r})$ denotes the spin density of the conduction electrons after switching on the Kondo coupling at time $t=0$. We present data obtained from a time-dependent numerical renormalisation group (TD-NRG) calculation. We gauge the accuracy of our two-band NRG by the spatial sum-rules of the equilibrium correlation functions and the reproduction of the analytically exactly known spin-correlation function of the decoupled Fermi sea. We find a remarkable building up of Kondo-correlation outside of the light cone defined by the Fermi velocity of the host metal. By employing a perturbative approach exact in second-order of the Kondo coupling, we connect these surprising correlations to the intrinsic spin-density entanglement of the Fermi sea. The thermal wave length supplies a cutoff scale at finite temperatures beyond which correlations are exponentially suppressed. We present data for the frequency dependent retarded spin-spin susceptibility and use the results to calculate the real-time response of a weak perturbation in linear response: within the spatial resolution no response outside of the light cone is found.

References in corpus (13)

• The numerical renormalization group method for quantum impurity systems
• Real-time dynamics in Quantum Impurity Systems: A Time-dependent Numerical Renormalization Group Approach
• Diagrammatic Monte Carlo simulation of non-equilibrium systems
• A Numerical Renormalization Group approach to Green's Functions for Quantum Impurity Models
• Spin Precession and Real Time Dynamics in the Kondo Model: A Time-Dependent Numerical Renormalization-Group Study
• On steady-state currents through nano-devices: a scattering-states numerical renormalization group approach to open quantum systems
• A perturbative nonequilibrium renormalization group method for dissipative quantum mechanics: Real-time RG in frequency space (RTRG-FS)
• Kondo resonances and anomalous gate dependence of electronic conduction in single-molecule transistors
• Kondo screening cloud in a one dimensional wire: Numerical renormalization group study
• Nonequilibrium Transport through a Kondo Dot in a Magnetic Field: Perturbation Theory
• Friedel oscillations and the Kondo screening cloud
• Hybrid NRG-DMRG approach to real-time dynamics of quantum impurity systems
• Transport in single-molecule transistors: Kondo physics and negative differential resistance

Cited by in corpus (33)

• Non-Hermitian Physics
• Solving quantum impurity problems in and out of equilibrium with variational approach
• Nonequilibrium, spatio-temporal formation of the Kondo screening-cloud on a lattice
• Voltage quench dynamics of a Kondo system
• The fate of the Kondo cloud in a superconductor
• Variational principle for quantum impurity systems in and out of equilibrium: application to Kondo problems
• Josephson-Kondo screening cloud in circuit quantum electrodynamics
• Multiple magnetic impurities on surfaces: Scattering and quasiparticle interference
• Entanglement-enhanced spreading of correlations
• Universal spatial correlations in the anisotropic Kondo screening cloud: analytical insights and numerically exact results from a coherent state expansion
• Bypassing the energy-time uncertainty in time-resolved photoemission
• Many-body theory of the neutralization of strontium ions on gold surfaces
• Effective low-energy description of the two impurity Anderson model: RKKY interaction and quantum criticality
• Strongly correlated multi-impurity models: The crossover from a single-impurity problem to lattice models
• Resolving the nonequilibrium Kondo singlet in energy- and position-space using quantum measurements
• Quench dynamics and relaxation of a spin coupled to interacting leads
• Quench dynamics of spin in quantum dots coupled to spin-polarized leads
• Realistic quantum critical point in one-dimensional two-impurity models
• Open Wilson chains for quantum impurity models: Keeping track of all bath modes
• Semi-group influence matrices for non-equilibrium quantum impurity models
• Ground-state properties of the symmetric single-impurity Anderson model on a ring from Density-Matrix Renormalization Group, Hartree-Fock, and Gutzwiller theory
• Decoherence of an entangled state of a strongly-correlated double quantum dot structure through tunneling processes
• Simulating realistic screening clouds around quantum impurities: role of spatial anisotropy and disorder
• Dynamics of the impurity screening cloud following quantum quenches of the Resonant Level Model
• Real-time dynamics induced by quenches across the quantum critical points in gapless Fermi systems with a magnetic impurity
• Efficient impurity-bath trial states from superposed Slater determinants
• Quench dynamics of the Kondo effect: transport across an impurity coupled to interacting wires
• Equilibrium and real-time properties of the spin correlation function in the two-impurity Kondo model
• Impurity with a resonance in the vicinity of the Fermi energy
• Underscreened Kondo Compensation in a Superconductor
• Ballistic Entanglement Cloud after a Boundary Quench
• Relaxation dynamics of a quantum spin coupled to a topological edge state
• Ground state overlap knows about ultraviolet dynamics: results for the Kondo model