We study the role of spin correlations in nonlinear absorption due to transitions from a deep impurity level to states above a Fermi sea. We demonstrate that the Hubbard repulsion between two electrons at the impurity leads to a logarithmic divergence in chi(3) at the absorption threshold. This divergence is a manifestation of the Kondo physics in the nonlinear optical response of Fermi sea systems. We also show that, for off-resonant pump excitation, the pump-probe spectrum exhibits a narrow peak below the linear absorption onset. Remarkably, the light-induced Kondo temperature, which governs the shape of the Kondo-absorption spectrum, can be tuned by varying the intensity and frequency of the pump.
We address the fundamental question how the spatial Kondo correlations are building up in time assuming an initially decoupled impurity spin ${\stackrel{P\vec}{S}}_{\mathrm{imp}}$. We investigate the time-dependent spin-correlation function $\ensuremath{\chi}(\stackrel{P\vec}{r},t)=\ensuremath{\langle}{\stackrel{P\vec}{S}}_{\mathrm{imp}}\stackrel{P\vec}{s}(\stackrel{P\vec}{r})\ensuremath{\rangle}(t)$ in the Kondo model with antiferromagnetic and ferromagnetic couplings, where $\stackrel{P\vec}{s}(\stackrel{P\vec}{r})$ 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 wavelength 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.
We investigate magnetic properties induced by a spinless impurity in strongly correlated electron systems, i.e., the Hubbard model in spatial dimension
D=1,2, and
3. For the one-dimensional (1D) system exploiting the Bethe ansatz exact solution we find that the spin susceptibility and the local density of states in the vicinity of a spinless impurity show divergent behaviors. The results imply that the induced local moment is not completely quenched at any finite temperatures. On the other hand, the spin lattice relaxation rate obtained by bosonization and boundary conformal field theory satisfies a relation analogous to the Korringa law, ${1/T}_{1}T\ensuremath{\sim}{\ensuremath{\chi}}^{2}.$ In the 2D and 3D systems, the analysis based upon the antiferromagnetically correlated Fermi liquid theory reveals that the antiferromagnetic spin fluctuation developed in the bulk is much suppressed in the vicinity of a spinless impurity, and thus magnetic properties are governed by the induced local moment, which leads to the Korringa law of
1/T1.We study the three-body Fermi liquid effects in the SU(
N) Anderson impurity model within the strong interaction limit $U\ensuremath{\rightarrow}\ensuremath{\infty}$, where the occupation number
Nd of the impurity levels varies over the range of
0<Nd<1. The three-body correlations arise among the impurity electrons when the electron-hole symmetry, the time-reversal symmetry, or both are broken by external fields or potentials. They play a key role in low-energy transport, particularly in the next-to-leading-order terms of power expansion with respect to temperature
T and bias voltage
eV. Using the numerical renormalization group approach, we calculate the differential conductance and nonlinear current noise through quantum dots, as well as the thermal conductivity of both quantum dots and magnetic alloys. Specifically, we focus on the SU(2) and SU(4) cases, demonstrating how the three-body correlations evolve in the strong interaction limit across the
1/N-filling Kondo regime at ${N}_{d}^{}\ensuremath{\simeq}1.0$ and the valence fluctuation regime where the occupation number
Nd varies rapidly with the position ${\ensuremath{\epsilon}}_{d}^{}$ of the impurity levels. We also show that the three-body correlations strongly couple with asymmetries in the tunnel couplings between quantum dots and reservoirs. For
N=4, this coupling significantly affects the order
(eV)3 nonlinear current through the quarter-filling Kondo state, where the electron-hole symmetry is broken. In particular, in the $U\ensuremath{\rightarrow}\ensuremath{\infty}$ limit, the expansion coefficients exhibit clear plateau structures associated with the Kondo effect at ${N}_{d}^{}\ensuremath{\simeq}1.0$. Our formulation and analysis pave the way for deducing the three-body correlations from the low-energy experiments on the next-to-leading-order transport.
We investigate magnetic properties induced by a spinless impurity in strongly correlated electron systems, i.e. the Hubbard model in the spatial dimension
D=1,2, and 3. For the 1D system exploiting the Bethe ansatz exact solution we find that the spin susceptibility and the local density of states in the vicinity of a spinless impurity show divergent behaviors. The results imply that the induced local moment is not completely quenched at any finite temperatures. On the other hand, the spin lattice relaxation rate obtained by bosonization and boundary conformal field theory satisfies a relation analogous to the Korringa law,
1/T1T∼χ2. In the 2D and 3D systems, the analysis based upon the antiferromagnetically correlated Fermi liquid theory reveals that the antiferromagnetic spin fluctuation developed in the bulk is much suppressed in the vicinity of a spinless impurity, and thus magnetic properties are governed by the induced local moment, which leads to the Korringa law of
1/T1.
The dynamics of the anisotropic Kondo model under the periodic driving is studied. The periodic driving we consider is the local magnetic field which couples with the impurity spin and the in-plane exchange interaction. At the special point in the parameter space (Toulouse limit), the anisotropic Kondo model can be transformed to the non-interacting resonant level model and thereby the exact results for arbitrary external fields can be obtained. It is shown that characteristic behavior of the dynamics changes with the field intensity, the field frequency, and the Kondo temperature. When the local magnetic field intensity is very large compared with the field frequency and the Kondo temperature, the time dependence of the impurity spin and the spin density of the fermionic bath shows an oscillation whose period is inversely proportional to the field intensity. We also find that another time scale, which is given by the inverse of the Kondo temperature, governs the response of the system to the external field.