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arXiv:2405.17348 · Nature Communications

Kondo-Zeno crossover in the dynamics of a monitored quantum dot

Matthieu Vanhoecke, Marco Schirò

Published Jul 4, 2025• 11 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1038/s41467-025-61287-y

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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.
This thesis focuses on the study of dissipative quantum impurity models. Quantum impurity models describe a localized quantum system, known as the impurity, that interacts with a large quantum bath, enabling the exploration of essential phenomena such as the Kondo effect in magnetic impurities and the transport properties in quantum dots. An intriguing extension of these models is the exploration of the interplay between strong correlations and dissipation. Dissipation, often described by the Lindblad master equation in its Markovian limit, introduces challenges and opportunities as it interacts with coherent many-body effects. In this thesis, we want to investigate the non-equilibrium dynamics of quantum impurity systems influenced by both strong correlations and dissipation across four main parts. We begin by developing numerical methods, specifically a diagrammatic Monte Carlo technique, to analyze the real-time dynamics of dissipative quantum impurity models. Our findings demonstrate that local Markovian dissipation enhances the convergence of Monte Carlo sampling by constraining the process to a reduced subspace of diagrams. This effectively mitigates the sign problem and facilitates the exploration of longer time scales compared to conventional unitary approaches. In the second part, we derive a self-consistent dynamical map using the Non-Crossing Approximation to study the long-term behavior of dissipative quantum impurity models. This method effectively resums diagrams into a self-consistent Dyson equation, capturing essential non-Markovian environmental effects, including the Kondo effect. In a third part, we examine the relationship between Kondo physics and Markovian dissipation by investigating an interacting quantum dot coupled to a metallic bath under continuous charge monitoring. We identify a crossover from Kondo screening to the Quantum Zeno effect, effectively described by a non-Hermitian Kondo model in the weak dissipation regime. Finally, the last part explores the effects of particle losses on the Kondo effect and the Kondo-Zeno crossover. Preliminary results indicate that while single-particle losses reduce many-body effects, two-body losses introduce intriguing phenomena, such as spin decay and hints of the Kondo-Zeno crossover, along with an unusual spectral function exhibiting a low-frequency lineshape.
We present a theoretical and numerical study of measurement-induced phase transitions and quantum Zeno dynamics in continuously monitored open many-body systems. Moving beyond closed unitary systems, we investigate the competition between chaotic unitary evolution and continuous weak measurements by employing the stochastic Schrödinger equation (quantum jump Monte Carlo) formalism and non-hermitian effective Hamiltonians. Our analysis examines the transition from area-law to volume-law entanglement scaling, mutual information properties, and the critical scaling hypothesis near the measurement-rate threshold. Furthermore, we derive original analytical estimates for the quantum correlation damping decrement in the regime of strong Zeno suppression and validate the theoretical findings using stochastic trajectory numerical simulation protocols with finite-size scaling.
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.
We study finite-size effect of the Kondo screening cloud in a double quantum dot setup via a large-NNN slave-boson mean-field theory. In this setup, one of the dots is embedded in a close metallic ring with a finite size LLL and the other dot is side coupled to the embedded dot via an antiferromagnetic spin-spin-exchange coupling with a strength KKK. The antiferromagnetic coupling favors local spin-singlet state and suppresses the Kondo screening. The mean-field phase diagram as a function of 1/L1/L1/L and KKK shows a crossover to the local spin-singlet ground state from the Kondo phase to occur at K<KcK<{K}_{c}K<Kc​ (L=4n,4n+1,4n+3)(L=4n,4n+1,4n+3)(L=4n,4n+1,4n+3) and at K>KcK>{K}_{c}K>Kc​ (L=4n+2)(L=4n+2)(L=4n+2). The effective Kondo temperature Tk{T}_{k}Tk​ (proptotional to inverse of the Kondo screening cloud size) shows the Kosterlitz-Thouless (KT) scaling at finite sizes for L=4n,4n+2L=4n,4n+2L=4n,4n+2, indicating quantum transition of the KT type between the Kondo screened phase for $K\ensuremath{\le}{K}_{c}$ and a local spin-singlet phase for $K\ensuremath{\ge}{K}_{c}$ in the thermodynamic limit with Kc{K}_{c}Kc​ being the critical value. The local density of states on the embedded quantum dot and the persistent current at finite sizes with different values of KKK are calculated in the crossover region.
We study the breakdown of Kondo screening by a local magnetic field from the perspective of a measurement-driven entanglement transition in a monitored quantum system. Here, the Kondo coupling leads to the growth in entanglement of an impurity spin with it's fermionic environment, while the local field plays the role of a continuous observer. Using a non-perturbative Unitary Renormalization Group (URG) approach, we derive coupled renormalization-group flow equations for the Kondo exchange and the local field, and obtain a field-dependent RG phase diagram. The RG flows separate a low-energy Kondo-screened phase, where the impurity is absorbed into the Fermi sea and forms an entangled singlet with the conduction bath, from a polarized local-moment phase in which screening is frustrated and impurity-bath entanglement is suppressed. We identify the fixed-point Hamiltonians governing the two phases and the critical regime, and relate the transition to the emergence of a novel non-Fermi liquid. Various impurity signatures such as the spectral function and thermalisation of impurity observables are used to characterise this entanglement transition. These results offer insight into the interplay of decoherence and measurement in governing the dynamics of a prototypical quantum system.
We consider evolution of a double quantum dot (DQD) two-electron spin qubit which is continuously weakly measured with a linear charge detector (quantum point contact). Since the interaction between the spins of two electrons depends on their charge state, the charge measurement affects the state of two spins, and induces non-trivial spin dynamics. We consider the regimes of strong and weak coupling to the detector, and investigate the measurement-induced spin dynamics both analytically and numerically. We observe emergence of the negative-result evolution and the system stabilization due to an analog of quantum Zeno effect. Moreover, unitary evolution between the triplet and a singlet state is induced by the negative-result measurement. We demonstrate that these effects exist for both strong and weak coupling between the detector and the DQD system.