Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2111.07771

Kondo Effect in a Quantum Dot under Continuous Quantum Measurement

Masahiro Hasegawa, Masaya Nakagawa, Keiji Saito

Published Nov 15, 2021• 0 citations
arXivHTMLPDF

Abstract

The backaction of quantum measurement on the Kondo effect in a quantum dot system is investigated by considering continuous projective measurement of singly occupied states of a quantum dot. We elucidate the qualitative feature of the Kondo effect under quantum measurement and determine effective Kondo temperature affected by the measurement. The Kondo resonance in the spectral function is suppressed when the measurement strength reaches the energy scale of the Kondo temperature without measurement. Through the spin susceptibility, we identify the generalized Kondo temperature under continuous quantum measurement. The measurement backaction changes the singularity in the spin susceptibility into a highly non-monotonic temperature dependence around the generalized Kondo temperature. The dependence of the generalized Kondo temperature on the measurement strength is quantitatively discussed.

DOI
10.48550/arxiv.2111.07771

Related papers

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

Matthieu Vanhoecke, Marco Schirò

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.

arXiv:2405.17348•Nature Communications•Jul 4, 2025•11 citations

Kondo effect out of equilibrium

Thomas Korb, Herbert Schoeller

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.

•Jan 1, 2006•0 citations

Anomalous Conductance of a Spin-1 Quantum Dot

Anna Posazhennikova, Piers Coleman

We interpret the recent observation of a zero-bias anomaly in spin-1 quantum dots in terms of an underscreened Kondo effect. Although spin-1 quantum dots are expected to undergo a two-stage quenching effect, in practice the log-normal distribution of Kondo temperatures leads to a broad temperature region dominated by underscreened Kondo physics. General arguments, based on the asymptotic decoupling between the partially screened moment and the leads, predict a singular temperature and voltage dependence of the conductance G and differential conductance g, resulting in dg/dT approximately 1/T and dG/dV approximately 1/V. Using a Schwinger boson approach, we show how these qualitative expectations are borne out in a detailed many body calculation.

arXiv:cond-mat/0410001•Physical Review Letters•Jan 26, 2005•49 citations

Robustness of the Kondo effect in a quantum dot coupled to Majorana zero modes

Joelson F. Silva, Luis G. G. V. Dias da Silva, E. Vernek

The prospect of using semiconductor quantum dots as an experimental tool to distinguish Majorana zero modes (MZMs) from other zero-energy excitations such as Kondo resonances has brought up the fundamental question of whether topological superconductivity and the Kondo effect can coexist in these systems. Here, we study the Kondo effect in a quantum dot coupled to a metallic contact and to a pair of MZMs. We consider a situation in which the MZMs are spin polarized in opposite directions. By using numerical renormalization group calculations and scaling analysis of the renormalization group equations, we show that the Kondo effect takes place at low temperatures, regardless of the coupling to the MZMs. Interestingly, we find that the Kondo singlet essentially decouples from the MZMs such that the residual impurity entropy can show local non-Fermi-liquid properties characteristic of the single Majorana excitations. This offers the possibility of tuning between Fermi-liquid and non-Fermi-liquid regimes simply by changing the quantum-dot-MZM couplings.

arXiv:1910.07026•Physical review. B./Physical review. B•Feb 25, 2020•26 citations

The Kondo Effect and Controlled Spin Entanglement in Coupled Double-Quantum-Dots

A. M. Chang

Semiconductor double‐quantum dots represent an ideal system for studying the novel spin physics of localized spins. On each quantum dot when the number of electrons is odd and the net spin is 1/2, a strong coupling of this localized spin to conducting electrons in the leads gives rise to Kondo correlation. On the other hand, in the coupled double‐quantum‐dot if the inter‐dot antiferromagnetic interaction is strong, the two spins can form a correlated spin‐singlet state, quenching the Kondo effect. This competition between Kondo and antiferromagnetic correlation is studied in a controlled manner by tuning the inter‐dot tunnel coupling. Increasing the inter‐dot tunneling, we observe a continuous transition from a single‐peaked to a double‐peaked Kondo resonance in the differential conductance. On the double‐peaked side, the differential conductance becomes suppressed at zero source‐drain bias. The observed strong suppression of the differential conductance at zero bias provides direct evidence signaling the formation of an entangled spin‐singlet state. This evidence for entanglement and the tunability of our devices bode well for quantum computation applications.

AIP conference proceedings•Jan 1, 2005•1 citation

Fidelity Susceptibility Perspective on the Kondo Effect and Impurity Quantum Phase Transitions

Lei Wang, Hiroshi Shinaoka, Matthias Troyer

The Kondo effect is a ubiquitous phenomenon appearing at low temperature in quantum confined systems coupled to a continuous bath. Efforts in understanding and controlling it have triggered important developments across several disciplines of condensed matter physics. A recurring pattern in these studies is that the suppression of the Kondo effect often results in intriguing physical phenomena such as impurity quantum phase transitions or non-Fermi-liquid behavior. We show that the fidelity susceptibility is a sensitive indicator for such phenomena because it quantifies the sensitivity of the system's state with respect to its coupling to the bath. We demonstrate the power of the fidelity susceptibility approach by using it to identify the crossover and quantum phase transitions in the one and two impurity Anderson models. The feasibility of measuring fidelity susceptibility in condensed matter as well as ultracold quantum gases experiments opens exciting new routes to diagnose the Kondo problem and impurity quantum phase transitions.

arXiv:1507.06991•Physical Review Letters•Dec 1, 2015•14 citations
The backaction of quantum measurement on the Kondo effect in a quantum dot system is investigated by considering continuous projective measurement of singly occupied states of a quantum dot. We elucidate the qualitative feature of the Kondo effect under quantum measurement and determine effective Kondo temperature affected by the measurement. The Kondo resonance in the spectral function is suppressed when the measurement strength reaches the energy scale of the Kondo temperature without measurement. Through the spin susceptibility, we identify the generalized Kondo temperature under continuous quantum measurement. The measurement backaction changes the singularity in the spin susceptibility into a highly non-monotonic temperature dependence around the generalized Kondo temperature. The dependence of the generalized Kondo temperature on the measurement strength is quantitatively discussed.
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.
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.
We interpret the recent observation of a zero-bias anomaly in spin-1 quantum dots in terms of an underscreened Kondo effect. Although spin-1 quantum dots are expected to undergo a two-stage quenching effect, in practice the log-normal distribution of Kondo temperatures leads to a broad temperature region dominated by underscreened Kondo physics. General arguments, based on the asymptotic decoupling between the partially screened moment and the leads, predict a singular temperature and voltage dependence of the conductance G and differential conductance g, resulting in dg/dT approximately 1/T and dG/dV approximately 1/V. Using a Schwinger boson approach, we show how these qualitative expectations are borne out in a detailed many body calculation.
The prospect of using semiconductor quantum dots as an experimental tool to distinguish Majorana zero modes (MZMs) from other zero-energy excitations such as Kondo resonances has brought up the fundamental question of whether topological superconductivity and the Kondo effect can coexist in these systems. Here, we study the Kondo effect in a quantum dot coupled to a metallic contact and to a pair of MZMs. We consider a situation in which the MZMs are spin polarized in opposite directions. By using numerical renormalization group calculations and scaling analysis of the renormalization group equations, we show that the Kondo effect takes place at low temperatures, regardless of the coupling to the MZMs. Interestingly, we find that the Kondo singlet essentially decouples from the MZMs such that the residual impurity entropy can show local non-Fermi-liquid properties characteristic of the single Majorana excitations. This offers the possibility of tuning between Fermi-liquid and non-Fermi-liquid regimes simply by changing the quantum-dot-MZM couplings.
Semiconductor double‐quantum dots represent an ideal system for studying the novel spin physics of localized spins. On each quantum dot when the number of electrons is odd and the net spin is 1/2, a strong coupling of this localized spin to conducting electrons in the leads gives rise to Kondo correlation. On the other hand, in the coupled double‐quantum‐dot if the inter‐dot antiferromagnetic interaction is strong, the two spins can form a correlated spin‐singlet state, quenching the Kondo effect. This competition between Kondo and antiferromagnetic correlation is studied in a controlled manner by tuning the inter‐dot tunnel coupling. Increasing the inter‐dot tunneling, we observe a continuous transition from a single‐peaked to a double‐peaked Kondo resonance in the differential conductance. On the double‐peaked side, the differential conductance becomes suppressed at zero source‐drain bias. The observed strong suppression of the differential conductance at zero bias provides direct evidence signaling the formation of an entangled spin‐singlet state. This evidence for entanglement and the tunability of our devices bode well for quantum computation applications.
The Kondo effect is a ubiquitous phenomenon appearing at low temperature in quantum confined systems coupled to a continuous bath. Efforts in understanding and controlling it have triggered important developments across several disciplines of condensed matter physics. A recurring pattern in these studies is that the suppression of the Kondo effect often results in intriguing physical phenomena such as impurity quantum phase transitions or non-Fermi-liquid behavior. We show that the fidelity susceptibility is a sensitive indicator for such phenomena because it quantifies the sensitivity of the system's state with respect to its coupling to the bath. We demonstrate the power of the fidelity susceptibility approach by using it to identify the crossover and quantum phase transitions in the one and two impurity Anderson models. The feasibility of measuring fidelity susceptibility in condensed matter as well as ultracold quantum gases experiments opens exciting new routes to diagnose the Kondo problem and impurity quantum phase transitions.