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arXiv:2406.03527 · Communications Physics

Dissipative realization of Kondo models

Martino Stefanini, Yi-Fan Qu, Tilman Esslinger, Sarang Gopalakrishnan, Eugene Demler, Jamir Marino

Published May 22, 2025• 13 citations
arXivHTMLPDF

Abstract

The Kondo effect is a prototypical strongly correlated phenomenon, and it is usually discussed in the context of unitary dynamics. Here, we demonstrate that the Kondo effect can be induced through non-linear dissipative channels, without requiring any coherent interaction on the impurity site. Specifically, we consider a reservoir of noninteracting fermions that can hop on a few impurity sites that are subjected to strong two-body losses. In the simplest case of a single lossy site, we recover the Anderson impurity model in the regime of infinite repulsion, with a small residual dissipation as a perturbation. While the Anderson model gives rise to the Kondo effect, this residual dissipation competes with it, offering an instance of a nonlinear dissipative impurity where the interplay between coherent and incoherent dynamics emerges from the same underlying physical process. We further outline how this dissipative engineering scheme can be extended to two or more lossy sites, realizing generalizations of the Kondo model with spin 1 or higher. Our results suggest alternative implementations of Kondo models using ultracold atoms in transport experiments, where localized dissipation can be naturally introduced, and the Kondo effect observed through conductance measurements.

DOI
10.1038/s42005-025-02141-x

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The Kondo effect is a prototypical strongly correlated phenomenon, and it is usually discussed in the context of unitary dynamics. Here, we demonstrate that the Kondo effect can be induced through non-linear dissipative channels, without requiring any coherent interaction on the impurity site. Specifically, we consider a reservoir of noninteracting fermions that can hop on a few impurity sites that are subjected to strong two-body losses. In the simplest case of a single lossy site, we recover the Anderson impurity model in the regime of infinite repulsion, with a small residual dissipation as a perturbation. While the Anderson model gives rise to the Kondo effect, this residual dissipation competes with it, offering an instance of a nonlinear dissipative impurity where the interplay between coherent and incoherent dynamics emerges from the same underlying physical process. We further outline how this dissipative engineering scheme can be extended to two or more lossy sites, realizing generalizations of the Kondo model with spin 1 or higher. Our results suggest alternative implementations of Kondo models using ultracold atoms in transport experiments, where localized dissipation can be naturally introduced, and the Kondo effect observed through conductance measurements.
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.
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 analyze the competition between strong correlations and dissipation in quantum impurity systems from the Kondo regime to the valence fluctuation regime by developing a slave-boson theory for a non-Hermitian Anderson impurity model with one-body loss. Notably, in the non-Hermitian Kondo regime, strong correlations qualitatively change the nature of dissipation through renormalization effects, where the effective one-body loss is suppressed and emergent many-body dissipation characterized by the complex-valued hybridization is generated. We unveil the mechanism of a dissipative quantum phase transition of the Kondo state on the basis of this renormalization effect, which counterintuitively enhances the lifetime of the impurity against loss. We also find a crossover from the non-Hermitian Kondo regime to the valence fluctuation regime dominated by one-body dissipation. Our results can be tested in a wide variety of setups such as quantum dots coupled to electronic leads and quantum point contacts in ultracold Fermi gases.
Simulating dissipative quantum many-body systems presents a significant theoretical challenge. Here, the authors develop an efficient nonperturbative framework that is tailored to dissipative impurity problems, combining a superposition of Gaussian states (SGS) variational ansatz with the quantum trajectory approach. They showcase the method with a model of a spinful impurity subject to two-body losses embedded in a fermionic bath, for which they explore the full crossover from weak to strong dissipation. Their approach captures the emergence of a loss-induced Kondo effect under strong dissipation, and reveals an exotic negative conductance phenomenon at intermediate loss rates.
The effects of interchannel scattering of conduction electrons by the impurity and repulsion of conduction electrons at the impurity site on the two-channel Kondo model are simultaneously considered in this paper. It is shown that these two perturbations will substantially modify the usual local non-Fermi liquid behavior of the two-channel Kondo model. With bosonization and unitary transformations we find that the system can be transformed into a single channel Kondo model with anisotropy between longitudinal and transverse exchange couplings. Whatever for originally antiferromagnetic or ferromagnetic isotropic coupling, the system always flows to strong-coupling limit, which exhibits local Fermi liquid behavior at low temperatures.
The Kondo effect in condensed-matter systems manifests itself most sharply in their transport measurements. Here we propose an analogous transport signature of the orbital Kondo effect realized with ultracold atoms. Our system consists of imbalanced Fermi seas of two components of fermions and an impurity atom of different species which is confined by an isotropic potential. We first apply a $\ensuremath{\pi}/2$ pulse to transform two components of fermions into two superposition states. Their interactions with the impurity atom then cause a ``transport'' of fermions from majority to minority superposition states, whose numbers can be measured after applying another $3\ensuremath{\pi}/2$ pulse. In particular, when the interaction of one component of fermions with the impurity atom is tuned close to a confinement-induced ppp-wave or higher partial-wave resonance, the resulting conductance is shown to exhibit the Kondo signature, i.e., universal logarithmic growth by lowering the temperature. The proposed transport measurement will thus provide a clear evidence of the orbital Kondo effect accessible in ultracold atom experiments and pave the way for developing new insights into Kondo physics.