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arXiv:2507.20779 · Physical Review Research

Nonequilibrium transport through an interacting monitored quantum dot

Daniel Werner, Matthieu Vanhoecke, Marco Schirò, Enrico Arrigoni

Published Jan 27, 2026• 1 citation
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Abstract

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.

DOI
10.1103/8h9h-m7ks

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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.
The Anderson impurity model is a paradigmatic example in the study of strongly correlated quantum systems and describes an interacting quantum dot coupled to electronic leads. Here we investigate its dynamics following a quantum quench based on matrix product state simulations. We examine the behavior of its impurity magnetization. Its relaxation allows us to extract the predicted scaling of the Kondo temperature as a function of the impurity-lead hybridization and quantum dot repulsion. Additionally, our simulations provide estimates of the currents in the nonequilibrium quasisteady state appearing after the quench. Through their values, we examine the dependence of the conductance on the voltage bias Vb{V}_{b}Vb​ and on the impurity chemical potential Vg{V}_{g}Vg​, which displays a zero-bias Kondo peak. Our results are relevant for transport measurements in Coulomb blockaded devices, and, in particular, in quantum dots induced in nanowires.
We study a dissipative version of the Anderson Impurity model, where an interacting impurity is coupled to a fermionic reservoir and exposed to Markovian dissipation in the form of two-body losses. Using a self-consistent hybridization expansion based on the Non-Crossing Approximation (NCA) we compute the dynamics of the impurity, its steady-state and spectral function. We show that the interplay between strong Coulomb repulsion and correlated dissipation gives rise to robust signatures of Kondo physics both at weak and strong losses. These include a strongly suppressed spin relaxation rate, displaying a characteristic Kondo-Zeno crossover and a spectral function where doublon band is quickly destroyed by dissipation while the coherent Kondo peak remains visible for weak losses, then disappears at intermediate values and finally re-emerge as the system enters in the Kondo-Zeno regime. As compared to the case of single particle losses we show that two-body dissipation protects Kondo physics. The picture obtained with NCA is confirmed by numerical simulations of exact dynamics on finite-size chains. We interpret these results using a dissipative Schrieffer-Wolff transformation, which leads to an effective Kondo model with residual impurity-bath losses which are suppressed by strong correlations or strong losses.
Correlations are a central ingredient of modern condensed matter physics. With the advent of mesoscopic physics, it became possible to study correlated systems in non-equilibrium situations, which can be reached by e.g. driving a constant current through a quantum dot. A basic question is how correlations on the one hand and a non-equilibrium current on the other hand influence each other. Here this interplay is studied for the model system of a quantum dot in the Kondo regime using the real time renormalization group (RTRG) method. This method is a functional renormalization group (RG) method allowing a non-perturbative description of correlated systems in non-equilibrium. For the Kondo quantum dot the method is generalized to the case of double vertices. The RTRG method not only provides equations for the calculation of the renormalized coupling between the quantum dot spin and the reservoir electrons, but also equations for the calculation of the non-equilibrium decoherence rate and the non-equilibrium current.The RG equations are derived to second order. This approximation is expected to be valid as long as the quantum dot does not enter the strong coupling regime, i.e. the effective coupling strength between the quantum dot spin and the electrons does not become too large. It is found that this is the case if the bias voltage applied to the dot or the temperature is much larger than the Kondo temperature.It is shown that the RG equations lead to coupling functions depending on the energy of the incident and the scattered electron. This dependence is simplified to the dependence on the average energy of the incident and the scattered electron in the weak coupling regime.A closer inspection of the RG equations for the couplings shows that they not only contain terms leading to a logarithmic increase of the coupling strength but also subleading terms which are unimportant in the weak coupling regime. The RG equations are solved analytically for the case where the subleading terms are neglected. It is found that the coupling functions develop resonances at energies associated with the chemical potentials of the reservoirs. The height of these resonances is determined by the decoherence rate. However, for bias voltages much larger than the Kondo temperature these resonances do not affect the conductance for a two terminal setup, so the conductance does not provide a measure for the decoherence rate in this case. It is found that the conductance for the two terminal setup is a universal function of voltage/Kondo temperature and temperature/Kondo temperature in the weak coupling regime. This function is calculated analytically in the limits of vanishing voltage or temperature. Furthermore, it is found that for zero temperature the decoherence rate is proportional to the non-equilibrium current flowing through the system. This supports the physical picture that a non-equilibrium current is associated with a decoherence rate, which cuts the logarithmic scaling of the coupling strength.Finally, the RG equations are solved numerically for zero temperature including the subleading corrections found before. As expected, the subleading corrections have no impact on the decoherence rate and the conductance in the weak coupling regime. On the other hand, it is found that they lead to strong deviations from the results of the analytic leading logarithmic approximation if the bias voltage approaches the Kondo temperature. Generally, it is found that the subleading corrections lead to a saturation of the decoherence rate and the conductance to some finite value. However, for the numerical solution a numerical regularization parameter has to be introduced. It turns out that the saturation value found depends on its value, so no statements on the precise value of the decoherence rate and the current can be made in this regime.
By nonperturbatively solving the nonequilibrium Anderson two-impurity model with the hierarchical equations of motion approach, we report a robust ferromagnetic (FM) phase in series-coupled double quantum dots, which can suppress the antiferromagnetic (AFM) phase and dominate the phase diagram at finite bias and detuning energy in the strongly correlated limit. The FM exchange interaction origins from the passive parallel spin arrangement caused by the Pauli exclusion principle during the electrons transport. At very low temperature, the Kondo screening of the magnetic moment in the FM phase induces some nonequilibrium Kondo effects in magnetic susceptibility, spectral functions and current. In the weakly correlated limit, the AFM phase is found still stable, therefore, a magnetic-field-free internal control of spin states can be expected through the continuous FM-AFM phase transition.
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Continuously monitoring a quantum system can strongly affect its properties and even suppress its coherent evolution via the Quantum Zeno effect. Here we focus on one of the simplest entangled many-body state, arising via the Kondo effect in a strongly interacting quantum dot coupled to a metallic bath, and investigate the effect of continuous monitoring of the dot total charge. We show that the decay rate of an initially polarized spin displays a crossover from Kondo screening to Quantum Zeno effect. Remarkably, the long-lived Kondo state is robust to weak dissipation, as confirmed by the dot spectral function which features a clear Kondo peak at finite dissipation, even in a regime where charge fluctuations and the associated Hubbard bands have been quenched by the monitoring protocol. We derive an effective model for the long-time dynamics which is described, at weak dissipation, by a non-Hermitian Kondo model. The continuous monitoring of entangled many-body states can strongly affect their properties. Here, the authors theoretically show a crossover from Kondo to Zeno screening for an interacting quantum dot coupled to a metallic bath with dissipation.