We apply a recently developed nonequilibrium real-time renormalization group method in frequency space to describe nonlinear quantum transport through a small fermionic quantum system coupled weakly to several reservoirs via spin and/or orbital fluctuations. We provide an analytic and well-controlled procedure to solve the RG equations in the weak-coupling regime. Within a 2-loop analysis, we derive analytic formulas for the nonlinear conductance and the kernel determining the time evolution of the reduced density matrix. Most importantly, we present a consistent formalism how the RG flow is cut off by relaxation and dephasing rates, which is necessary to calculate the precise line shape at resonances. We apply the general formalism to the nonequilibrium anisotropic Kondo model at finite magnetic field. We consider the weak-coupling regime, where the maximum of voltage and bare magnetic field is larger than the Kondo-temperature. In this regime, we calculate the nonlinear conductance, the magnetic susceptibility, the renormalized spin relaxation and dephasing rates, and the renormalized g-factor. All quantities are considered up to the first logarithmic contributions at resonance. Up to a redefinition of the Kondo temperature, we confirm previous results for the conductance and the magnetic susceptibility in the isotropic case. In addition, we present a consistent calculation of the line shape at the resonances, including the determination which rate cuts off the logarithmic divergence. Furthermore, we calculate the rates and the renormalized g-factor in nonequilibrium beyond leading order, being quantities characterizing the exponential decay of the time evolution of the magnetization. For all quantities we analyse also the anisotropic case and find interesting nonequilibrium effects at resonance.
We extend a perturbative, nonequilibrium renormalization group approach to multi-orbital systems and apply it for studying transport through two parallel quantum dots coupled electrostatically. In general, the conductance shows pronounced Kondoesque peaks at three voltages. One of these peaks disappears if, as in some experiments, one of the dots is decoupled from one of the two leads. For an asymmetric coupling to the leads, also negative differential conductances are possible. This is a genuine nonequilibrium effect, accompanying the Kondoesque peaks. Moreover, a criterion to distinguish spi…
A leading candidate for experimental confirmation of the non-local quantum dynamics of Majorana fermions is the topological Kondo effect, predicted for mesoscopic superconducting islands connected to metallic leads. We identify an anisotropic, Toulouse-like, limit of the topological Kondo problem where the full nonequilibrium conductance and shot noise can be calculated exactly. Near the Kondo fixed point, we find novel asymptotic features including a universal conductance scaling function, and fractional charge quantisation observable via the Fano factor. In the universal regime, our results …
In the previous paper, we found a series expression for the average electric current following a quench in the nonequilibrium Kondo model driven by a bias voltage. Here, we evaluate the steady state current in the regimes of strong and weak coupling. We obtain the standard leading order results in the usual weak antiferromagnetic regime, and we also find a new universal regime of strong ferromagnetic coupling with Kondo temperature $T_K = D e^{\frac{3π^2}{8} ρJ}$. In this regime, the differential conductance $dI/dV$ reaches the unitarity limit $2e^2/h$ asymptotically at large voltage or temper…
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 sp…
The Kondo effect, a hallmark of strong correlation physics, is characterized by the formation of an extended cloud of singlet states around magnetic impurities at low temperatures. While many implications of the Kondo cloud's existence have been verified, the existence of the singlet cloud itself has not been directly demonstrated. We suggest a route for such a demonstration by considering an observable that has no classical analog, but is still experimentally measurable: "singlet weights", or projections onto particular entangled two-particle states. Using approximate theoretical arguments, w…
In this work we analyze the nonequilibrium transport through a quantum impurity (quantum dot or molecule) attached to ferromagnetic leads by using a hybrid numerical renormalization group-time-dependent density matrix renormalization group thermofield quench approach.For this, we study the bias dependence of the differential conductance through the system, which shows a finite zero-bias peak, characteristic of the Kondo resonance and reminiscent of the equilibrium local density of states. In the non-equilibrium settings, the resonance in the differential conductance is also found to decrease w…
We theoretically study the nonequilibrium thermoelectric transport properties of a strongly-correlated molecule (or quantum dot) embedded in a tunnel junction. Assuming that the coupling of the molecule to the contacts is asymmetric, we determine the nonlinear current driven by the voltage and temperature gradients by using the perturbation theory. However, the subsystem consisting of the molecule strongly coupled to one of the contacts is solved by using the numerical renormalization group method, which allows for accurate description of Kondo correlations. We study the temperature gradient a…
We study the single-impurity Anderson model out of equilibrium under the influence of a bias voltage $ϕ$ and a magnetic field $B$. We investigate the interplay between the shift ($ω_B$) of the Kondo peak in the spin-resolved density of states (DOS) and the one ($ϕ_B$) of the conductance anomaly. In agreement with experiments and previous theoretical calculations we find that, while the latter displays a rather linear behavior with an almost constant slope as a function of $B$ down to the Kondo scale, the DOS shift first features a slower increase reaching the same behavior as $ϕ_B$ only for $|…
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-evo…
Inelastic spin flip excitations associated with single-ion magnetic anisotropy of quantum spins, can be strongly renormalized by Kondo exchange coupling to the conduction electrons in the substrate, as shown recently for the case of Co adatoms on CuN$_2$ islands. In this case differential conductance spectra show zero-bias anomalies due to a Kondo effect of the doubly degenerate ground state, and finite-bias step features due to spin flip excitations. Here I consider spin-1 quantum magnets with positive uniaxial anisotropy, where the ground state is non-degenerate and hence the Kondo effect do…
Nonequilibrium transport through an interacting monitored quantum dot
Institute of Theoretical and Computational Physics, Graz University of Technology（格拉茨工业大学理论与计算物理研究所）；JEIP, UAR 3573 CNRS, Collège de France, PSL Research University（法国国家科学研究中心联合研究单位3573 JEIP，法兰西学院，巴黎文理研究大学）
Quantum transport is studied for the nonequilibrium Anderson impurity model at zero temperature employing the multilayer multiconfiguration time-dependent Hartree theory within the second quantization representation (ML-MCTDH-SQR) of Fock space. To adress both linear and nonlinear conductance in the Kondo regime, two new techniques of the ML-MCTDH-SQR simulation methodology are introduced: (i) the use of correlated initial states, which is achieved by imaginary time propagation of the overall Hamiltonian at zero voltage and (ii) the adoption of the logarithmic discretization of the electronic …
Inelastic effects in molecular junctions in the Coulomb and Kondo regimes: Nonequilibrium equation-of-motion approach
在一个简单的非平衡运动方程（EOM）的方法被认为是在库仑阻塞和近藤制度的电子输运通过分子结的非弹性效应。该方案是自洽的，并且可以定性地再现库仑阻塞中振动特征的主要实验观察[H.Park et al.，Nature 407，57（2000）]和Kondo [L. H. Yu等人，物理修订信函93，266802（2004）]制度。考虑类似于Meir等人的平衡EOM方法[Phys. Rev. Lett. 66，3048（1991）;同上，70，2601（1993）]用于Keldysh等值线以说明结的非平衡性质，并且通过适当的Franck-Condon（FC）因子进行修整以说明振动特征。Meir等人的平衡EOM方案的结果在适当的限度内重现。
We study a $3$-level quantum dot in the singly occupied cotunneling regime coupled via a generic tunneling matrix to several multi-channel leads in equilibrium or nonequilibrium. We derive an effective model where also each reservoir has three channels labelled by the quark flavors $u$, $d$ and $s$ with an effective d.o.s. polarized w.r.t. an eight-dimensional $F$-spin corresponding to the eight generators of $SU(3)$. In equilibrium we perform a standard poor man scaling analysis and show that tunneling via virtual intermediate states induces flavor fluctuations on the dot which become $SU(3)$…
