Dephasing by Kondo impurities: Exact results

Using detailed balance and scaling properties of integrals that appear in the Coulomb gas reformulation of quantum impurity problems, we establish exact relations between the nonequilibrium quantum decay rates of the boundary sine-Gordon and the anisotropic Kondo model at zero temperature. Combining these results with findings from the thermodynamic Bethe ansatz, we derive exact closed form expressions for the quantum decay rate of the dissipative two-state system in the scaling limit. These expressions illustrate how the crossover from weak to strong tunneling takes place. We trace out the regimes in which the usually applied Golden Rule (nonadiabatic) rate expression fails. Using a conjectured correspondence between the relaxation and dephasing rate, we obtain the exact lower bound of the dephasing rate as a function of bias and dissipation strength.Using detailed balance and scaling properties of integrals that appear in the Coulomb gas reformulation of quantum impurity problems, we establish exact relations between the nonequilibrium quantum decay rates of the boundary sine-Gordon and the anisotropic Kondo model at zero temperature. Combining these results with findings from the thermodynamic Bethe ansatz, we derive exact closed form expressions for the quantum decay rate of the dissipative two-state system in the scaling limit. These expressions illustrate how the crossover from weak to strong tunneling takes place. We trace out the regimes in which the usually applied Golden Rule (nonadiabatic) rate expression fails. Using a conjectured correspondence between the relaxation and dephasing rate, we obtain the exact lower bound of the dephasing rate as a function of bias and dissipation strength.

arXiv:cond-mat/0211046Nov 3, 20020 citations

DEPHASING IN KONDO SYSTEMS: COMPARISON BETWEEN THEORY AND EXPERIMENT

F. Mallet, F. Schopfer, JERRY ERICSSON +4 more

International Symposium on Mesoscopic Superconductivity and Spintronics (MS+S)Oct 1, 20080 citations

Study on Quantum Criticality in a Dilute Kondo System

Takayuki Shiino, 貴之椎野

Mar 25, 20190 citations

Nonequilibrium transport through an interacting monitored quantum dot

Daniel Werner, Matthieu Vanhoecke, Marco Schirò +1 more

We study the interplay between strong correlations and Markovian dephasing, resulting from monitoring the charge or spin degrees of freedom of a quantum dot described by a dissipative Anderson impurity model. Using the auxiliary master equation approach, we compute the steady-state spectral function and occupation of the dot and discuss the role of dephasing on Kondo physics. Furthermore, we consider a two-lead setup that allows to compute the steady-state current and conductance. We show that the Kondo steady state is robust to moderate charge dephasing but not to spin dephasing, which we interpret in terms of dephasing-induced heating of low-energy excitations. Finally, we show universal scaling collapse of the nonlinear conductance with a dephasing-dependent Kondo scale.We study the interplay between strong correlations and Markovian dephasing, resulting from monitoring the charge or spin degrees of freedom of a quantum dot described by a dissipative Anderson impurity model. Using the auxiliary master equation approach, we compute the steady-state spectral function and occupation of the dot and discuss the role of dephasing on Kondo physics. Furthermore, we consider a two-lead setup that allows to compute the steady-state current and conductance. We show that the Kondo steady state is robust to moderate charge dephasing but not to spin dephasing, which we interpret in terms of dephasing-induced heating of low-energy excitations. Finally, we show universal scaling collapse of the nonlinear conductance with a dephasing-dependent Kondo scale.

arXiv:2507.20779Physical Review ResearchJan 27, 20261 citation

TWO KONDO IMPURITY PROBLEM: RELEVANCE TO HEAVY FERMIONS

Barbara Jones, C. M. Varma

Elsevier eBooksJan 1, 19871 citation

Spin precession and real-time dynamics in the Kondo model: Time-dependent numerical renormalization-group study

Frithjof B. Anders, Avraham Schiller

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. Comparisons with exact analytical results for the charge relaxation in the resonant-level model and for dephasing in the spin-boson model establish the accuracy of the method. The real-time dynamics of a single spin coupled to each type of bath 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 are 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 transient spin decay is described by the scaling variable $x=2{\ensuremath{\rho}}_{F}\ensuremath{\mid}J(T)\ensuremath{\mid}Tt$. In the antiferromagnetic regime, the long-time decay is governed for $T<{T}_{K}$ by the Kondo time scale $1∕{T}_{K}$ . Here ${\ensuremath{\rho}}_{F}$ is the conduction-electron density of states, ${T}_{K}$ is the Kondo temperature, and $J(T)$ is the effective exchange coupling at temperature $T$ . Results for spin precession are obtained by rotating the external magnetic field from the $x$ axis to the $z$ axis.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. Comparisons with exact analytical results for the charge relaxation in the resonant-level model and for dephasing in the spin-boson model establish the accuracy of the method. The real-time dynamics of a single spin coupled to each type of bath 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 are 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 transient spin decay is described by the scaling variable $x=2{\ensuremath{\rho}}_{F}\ensuremath{\mid}J(T)\ensuremath{\mid}Tt$. In the antiferromagnetic regime, the long-time decay is governed for $T<{T}_{K}$ by the Kondo time scale $1∕{T}_{K}$. Here ${\ensuremath{\rho}}_{F}$ is the conduction-electron density of states, ${T}_{K}$ is the Kondo temperature, and $J(T)$ is the effective exchange coupling at temperature $T$. Results for spin precession are obtained by rotating the external magnetic field from the $x$ axis to the $z$ axis.

arXiv:cond-mat/0604517Physical Review BDec 18, 2006250 citations

J

. In the ferromagnetic regime, the transient spin decay is described by the scaling variable $x=2{\ensuremath{\rho}}_{F}\ensuremath{\mid}J(T)\ensuremath{\mid}Tt$. In the antiferromagnetic regime, the long-time decay is governed for

T<{T}_{K}

by the Kondo time scale

1∕{T}_{K}

. Here ${\ensuremath{\rho}}_{F}$ is the conduction-electron density of states,

{T}_{K}

is the Kondo temperature, and

J(T)

is the effective exchange coupling at temperature

T

. Results for spin precession are obtained by rotating the external magnetic field from the

x

axis to the

z

axis.