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Register a new userNonequilibrium Kondo effect by equilibrium numerical renormalization group method: The hybrid Anderson model subject to a finite spin bias
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We investigate Kondo correlations in a quantum dot with normal and superconducting electrodes, where a spin bias voltage is applied across the device and the local interaction $U$ is either attractive or repulsive. When the spin current is blockaded in the large-gap regime, this nonequilibrium strongly-correlated problem maps into an equilibrium model solvable by the numerical renormalization group method. The Kondo spectra with characteristic splitting due to the nonequilibrium spin accumulation are thus obtained at high precision. It is shown that while the bias-induced decoherence of the spin Kondo effect is partially compensated by the superconductivity, the charge Kondo effect is enhanced out of equilibrium and undergoes an additional splitting by the superconducting proximity effect, yielding four Kondo peaks in the local spectral density. In the charge Kondo regime, we find a universal scaling of charge conductance in this hybrid device under different spin biases. The universal conductance as a function of the coupling to the superconducting lead is peaked at and hence directly measures the Kondo temperature. Our results are of direct relevance to recent experiments realizing negative-$U$ charge Kondo effect in hybrid oxide quantum dots [Nat. Commun. textbf{8}, 395 (2017)].
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The tunneling conductance is calculated as a function of the gate voltage in wide temperature range for the single quantum dot systems with Coulomb interaction. We assume that two orbitals are active for the tunneling process. We show that the Kondo temperature for each orbital channel can be largely different. The tunneling through the Kondo resonance almost fully develops in the region $T lsim 0.1 T_{K}^{*} sim 0.2 T_{K}^{*}$, where $T_{K}^{*}$ is the lowest Kondo temperature when the gate voltage is varied. At high temperatures the conductance changes to the usual Coulomb oscillations type. In the intermediate temperature region, the degree of the coherency of each orbital channel is different, so strange behaviors of the conductance can appear. For example, the conductance once increases and then decreases with temperature decreasing when it is suppressed at T=0 by the interference cancellation between different channels. The interaction effects in the quantum dot systems lead the sensitivities of the conductance to the temperature and to the gate voltage.
We show how the density-matrix numerical renormalization group (DM-NRG) method can be used in combination with non-Abelian symmetries such as SU(N), where the decomposition of the direct product of two irreducible representations requires the use of a so-called outer multiplicity label. We apply this scheme to the SU(3) symmetrical Anderson model, for which we analyze the finite size spectrum, determine local fermionic, spin, superconducting, and trion spectral functions, and also compute the temperature dependence of the conductance. Our calculations reveal a rich Fermi liquid structure.
We present here the details of a method [A. B. Culver and N. Andrei, Phys. Rev. B 103, L201103 (2021)] for calculating the time-dependent many-body wavefunction that follows a local quench. We apply the method to the voltage-driven nonequilibrium Kondo model to find the exact time-evolving wavefunction following a quench where the dot is suddenly attached to the leads at $t=0$. The method, which does not use Bethe ansatz, also works in other quantum impurity models and may be of wider applicability. We show that the long-time limit (with the system size taken to infinity first) of the time-evolving wavefunction of the Kondo model is a current-carrying nonequilibrium steady state that satisfies the Lippmann-Schwinger equation. We show that the electric current in the time-evolving wavefunction is given by a series expression that can be expanded either in weak coupling or in strong coupling, converging to all orders in the steady-state limit in either case. The series agrees to leading order with known results in the well-studied regime of weak antiferromagnetic coupling and also reveals a universal regime of strong ferromagnetic coupling with Kondo temperature $T_K^{(F)} = D e^{-frac{3pi^2}{8} rho |J|}$ ($J<0$, $rho|J|toinfty$). In this regime, the differential conductance $dI/dV$ reaches the unitarity limit $2e^2/h$ asymptotically at large voltage or temperature.
The spatial length of the Kondo screening is still a controversial issue related to Kondo physics. While renormalization group and Bethe Anzats solutions have provided detailed information about the thermodynamics of magnetic impurities, they are insufficient to study the effect on the surrounding electrons, i.e., the spatial range of the correlations created by the Kondo effect between the localized magnetic moment and the conduction electrons. The objective of this work is to present a quantitative way of measuring the extension of these correlations by studying their effect directly on the local density of states (LDOS) at arbitrary distances from the impurity. The numerical techniques used, the Embedded Cluster Approximation, the Finite U Slave Bosons, and Numerical Renormalization Group, calculate the Green functions in real space. With this information, one can calculate how the local density of states away from the impurity is modified by its presence, below and above the Kondo temperature, and then estimate the range of the disturbances in the non-interacting Fermi sea due to the Kondo effect, and how it changes with the Kondo temperature $T_{rm K}$. The results obtained agree with results obtained through spin-spin correlations, showing that the LDOS captures the phenomenology of the Kondo cloud as well. To the best of our knowledge, it is the first time that the LDOS is used to estimate the extension of the Kondo cloud.
Local three- and four-point correlators yield important insight into strongly correlated systems and have many applications. However, the non-perturbative, accurate computation of multipoint correlators is challenging, particularly in the real-frequency domain for systems at low temperatures. In an accompanying paper, we introduce generalized spectral representations for multipoint correlators. Here, we develop a numerical renormalization group (NRG) approach, capable of efficiently evaluating these spectral representations, to compute local three- and four-point correlators of quantum impurity models. The key objects in our scheme are partial spectral functions, encoding the systems dynamical information. Their computation via NRG allows us to simultaneously resolve various multiparticle excitations down to the lowest energies. By subsequently convolving the partial spectral functions with appropriate kernels, we obtain multipoint correlators in the imaginary-frequency Matsubara, the real-frequency zero-temperature, and the real-frequency Keldysh formalisms. We present exemplary results for the connected four-point correlators of the Anderson impurity model, and for resonant inelastic x-ray scattering (RIXS) spectra of related impurity models. Our method can treat temperatures and frequencies -- imaginary or real -- of all magnitudes, from large to arbitrarily small ones.
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