Chinese Physics Letters

Evolution of Spin and Charge in a System with Interacting Impurity and Conducting Electrons

张永梅, 熊诗杰

Published Jan 1, 2003• 0 citations

Abstract

We investigate the dynamics of spin and charge in an interacting system consisting of impurity and conduct-ing electrons. The time evolution of spin and charge in the impurity is given by solving the time-dependent Schroedinger equations for the many-body states of the interacting system. By switching on the interaction be-tween impurity and conducting electrons, the spin and charge of the impurity begin oscillations with frequencies that reflect the elementary excitations of the interacting system. The dynamics reflects the basic picture of the Kondo effect.

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Chinese Physics Letters

Evolution of Spin and Charge in a System with Interacting Impurity and Conducting Electrons

张永梅, 熊诗杰

Published Jan 1, 2003• 0 citations

OpenAlex

Abstract

Related papers

Evolution of Spin and Charge in a System with Interacting Impurity and Conducting Electrons

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We investigate the dynamics of spin and charge in an interacting system consisting of impurity and conducting electrons. The time evolution of spin and charge in the impurity is given by solving the time-dependent Schrödinger equations for the many-body states of the interacting system. By switching on the interaction between impurity and conducting electrons, the spin and charge of the impurity begin oscillations with frequencies that reflect the elementary excitations of the interacting system. The dynamics reflects the basic picture of the Kondo effect.We investigate the dynamics of spin and charge in an interacting system consisting of impurity and conducting electrons. The time evolution of spin and charge in the impurity is given by solving the time-dependent Schrödinger equations for the many-body states of the interacting system. By switching on the interaction between impurity and conducting electrons, the spin and charge of the impurity begin oscillations with frequencies that reflect the elementary excitations of the interacting system. The dynamics reflects the basic picture of the Kondo effect.

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Benedikt Lechtenberg, Frithjof B. Anders

We investigate the equilibrium and real-time properties of the spin-correlation function $\ensuremath{\langle}{\stackrel{P\vec}{S}}_{1}{\stackrel{P\vec}{S}}_{2}\ensuremath{\rangle}$ in the two-impurity Kondo model for different distances $R$ between the two-impurity spins. It is shown that the competition between the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction and the Kondo effect governs the amplitude of $\ensuremath{\langle}{\stackrel{P\vec}{S}}_{1}{\stackrel{P\vec}{S}}_{2}\ensuremath{\rangle}$. For distances $R$ exceeding the Kondo length scale, the Kondo effect also has a profound effect on the sign of the correlation function. For ferromagnetic Heisenberg couplings $J$ between the impurities and the conduction band, the Kondo effect is absent and the correlation function only decays for distances beyond a certain length scale introduced by finite temperature. The real-time dynamics after a sudden quench of the system reveals that correlations propagate through the conduction band with Fermi velocity. We identify two distinct timescales for the long-time behavior, which reflects that for small $J$ the system is driven by the RKKY interaction while for large $J$ the Kondo effect dominates. Interestingly, we find that at certain distances a one-dimensional dispersion obeying $\ensuremath{\epsilon}(k)=\ensuremath{\epsilon}(\ensuremath{-}k)$ may lead to a local parity conservation of the impurities such that $\ensuremath{\langle}{\stackrel{P\vec}{S}}_{1}{\stackrel{P\vec}{S}}_{2}\ensuremath{\rangle}$ becomes a conserved quantity for long times and does not decay to its equilibrium value.We investigate the equilibrium and real-time properties of the spin-correlation function $\ensuremath{\langle}{\stackrel{P\vec}{S}}_{1}{\stackrel{P\vec}{S}}_{2}\ensuremath{\rangle}$ in the two-impurity Kondo model for different distances $R$ between the two-impurity spins. It is shown that the competition between the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction and the Kondo effect governs the amplitude of $\ensuremath{\langle}{\stackrel{P\vec}{S}}_{1}{\stackrel{P\vec}{S}}_{2}\ensuremath{\rangle}$. For distances $R$ exceeding the Kondo length scale, the Kondo effect also has a profound effect on the sign of the correlation function. For ferromagnetic Heisenberg couplings $J$ between the impurities and the conduction band, the Kondo effect is absent and the correlation function only decays for distances beyond a certain length scale introduced by finite temperature. The real-time dynamics after a sudden quench of the system reveals that correlations propagate through the conduction band with Fermi velocity. We identify two distinct timescales for the long-time behavior, which reflects that for small $J$ the system is driven by the RKKY interaction while for large $J$ the Kondo effect dominates. Interestingly, we find that at certain distances a one-dimensional dispersion obeying $\ensuremath{\epsilon}(k)=\ensuremath{\epsilon}(\ensuremath{-}k)$ may lead to a local parity conservation of the impurities such that $\ensuremath{\langle}{\stackrel{P\vec}{S}}_{1}{\stackrel{P\vec}{S}}_{2}\ensuremath{\rangle}$ becomes a conserved quantity for long times and does not decay to its equilibrium value.

arXiv:1805.04254Physical review. B./Physical review. BJul 6, 20185 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.

R

between the two-impurity spins. It is shown that the competition between the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction and the Kondo effect governs the amplitude of $\ensuremath{\langle}{\stackrel{P\vec}{S}}_{1}{\stackrel{P\vec}{S}}_{2}\ensuremath{\rangle}$. For distances

R

exceeding the Kondo length scale, the Kondo effect also has a profound effect on the sign of the correlation function. For ferromagnetic Heisenberg couplings

J

between the impurities and the conduction band, the Kondo effect is absent and the correlation function only decays for distances beyond a certain length scale introduced by finite temperature. The real-time dynamics after a sudden quench of the system reveals that correlations propagate through the conduction band with Fermi velocity. We identify two distinct timescales for the long-time behavior, which reflects that for small

J

the system is driven by the RKKY interaction while for large

J

the Kondo effect dominates. Interestingly, we find that at certain distances a one-dimensional dispersion obeying $\ensuremath{\epsilon}(k)=\ensuremath{\epsilon}(\ensuremath{-}k)$ may lead to a local parity conservation of the impurities such that $\ensuremath{\langle}{\stackrel{P\vec}{S}}_{1}{\stackrel{P\vec}{S}}_{2}\ensuremath{\rangle}$ becomes a conserved quantity for long times and does not decay to its equilibrium value.