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.
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.
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.
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 the competition between Kondo physics and dissipation within an Anderson model of a magnetic impurity level that hybridizes with a metallic host and is also coupled, via the impurity charge, to the displacement of a bosonic bath having a spectral density proportional to ${\ensuremath{\omega}}^{s}$. As the impurity-bath coupling increases from zero, the effective Coulomb interaction between two electrons in the impurity level is progressively renormalized from its repulsive bare value until it eventually becomes attractive. For weak hybridization, this renormalization in turn produces a crossover from a conventional spin-sector Kondo effect to a charge Kondo effect. At particle-hole symmetry, and for sub-Ohmic bath exponents 0<s<1, further increase in the impurity-bath coupling results in a continuous zero-temperature transition to a broken-symmetry phase in which the ground-state impurity occupancy ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{n}}_{d}$ acquires an expectation value ${⟨{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{n}}_{d}⟩}_{0}\ensuremath{\ne}1$. The response of the impurity occupancy to a locally applied electric potential features the hyperscaling of critical exponents and $\ensuremath{\omega}∕T$ scaling that are expected at an interacting critical point. The numerical values of the critical exponents suggest that the transition lies in the same universality class as that of the sub-Ohmic spin-boson model. For the Ohmic case s=1, the transition is instead of Kosterlitz-Thouless type. Away from particle-hole symmetry, the quantum phase transition is replaced by a smooth crossover but signatures of the symmetric quantum critical point remain in the physical properties at elevated temperatures and/or frequencies.
We address the phenomenon of critical Kondo destruction in pseudogap Bose-Fermi Anderson and Kondo quantum impurity models. These models describe a localized level coupled both to a fermionic bath having a density of states that vanishes like ${|\ensuremath{\epsilon}|}^{r}$ at the Fermi energy ($\ensuremath{\epsilon}=0$) and, via one component of the impurity spin, to a bosonic bath having a sub-Ohmic spectral density proportional to ${|\ensuremath{\omega}|}^{s}$. Each bath is capable by itself of suppressing the Kondo effect at a continuous quantum phase transition. We study the interplay between these two mechanisms for Kondo destruction using continuous-time quantum Monte Carlo for the pseudogap Bose-Fermi Anderson model with 0<r<21 and $\frac{1}{2}\ensuremath{\le}s<1$, and applying the numerical renormalization group to the corresponding Kondo model. At particle-hole symmetry, the models exhibit a quantum-critical point between a Kondo (fermionic strong-coupling) phase and a localized (Kondo-destroyed) phase. The two solution methods, which are in good agreement in their domain of overlap, provide access to the many-body spectrum, as well as to correlation functions including, in particular, the single-particle Green's function and the static and dynamical local spin susceptibilities. The quantum-critical regime exhibits the hyperscaling of critical exponents and $\ensuremath{\omega}/T$ scaling in the dynamics that characterize an interacting critical point. The (r,s) plane can be divided into three regions: one each in which the calculated critical properties are dominated by the bosonic bath alone or by the fermionic bath alone, and between these two regions, a third in which the bosonic bath governs the critical spin response but both baths influence the renormalization-group flow near the quantum-critical point.
We study a pseudogap Anderson-Holstein model of a magnetic impurity level that hybridizes with a conduction band whose density of states vanishes in power-law fashion at the Fermi energy, and couples, via its charge, to a nondispersive bosonic mode (e.g., an optical phonon). The model, which we treat using poor-man's scaling and the numerical renormalization group, exhibits quantum phase transitions of different types depending on the strength of the impurity-boson coupling. For weak impurity-boson coupling, the suppression of the density of states near the Fermi energy leads to quantum phase transitions between strong-coupling (Kondo) and local-moment phases. For sufficiently strong impurity-boson coupling, however, the bare repulsion between a pair of electrons in the impurity level becomes an effective attraction, leading to quantum phase transitions between strong-coupling (charge Kondo) and local-charge phases. Even though the Hamiltonian exhibits different symmetries in the spin and charge sectors, the thermodynamic properties near the two types of quantum phase transition are closely related under spin-charge interchange. Moreover, the critical responses to a local magnetic field (for small impurity-boson coupling) and to an electric potential (for large impurity-boson coupling) are characterized by the same exponents, whose values place these quantum-critical points in the universality class of the pseudogap Anderson model. One specific case of the pseudogap Anderson-Holstein model may be realized in a double-quantum-dot device, where the quantum phase transitions manifest themselves in the finite-temperature linear electrical conductance.