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arXiv:2205.09789 · Physical review. B./Physical review. B

Kondo nanomechanical dissipation in the driven Anderson impurity model

Lucas Kohn, Giuseppe E. Santoro, Michele Fabrizio, Erio Tosatti

Published Jan 17, 2023• 1 citation
arXivHTMLPDF

Abstract

The cyclic sudden switch of a magnetic impurity from a Kondo to a non-Kondo state and back was recently proposed to involve an important dissipation of the order of several ${k}_{B}{T}_{K}$ per cycle. The possibility to reveal this and other electronic processes through nanomechanical dissipation by, e.g., ultrasensitive atomic force microscope (AFM) tools would represent an unusual and interesting form of spectroscopy. Here, we explore the dependence on the switching time of the expected dissipation, a quantity whose magnitude is physically expected to drop from maximum to zero between sudden and slow switching, respectively. As an application of a recently established matrix-product-state-based time-dependent variational algorithm, we study the magnetic-field-induced Kondo switching in an Anderson model of the magnetic impurity. We find, quite reasonably, that dissipation requires switching within the Kondo timescale $\ensuremath{\hbar}{({k}_{B}{T}_{K})}^{\ensuremath{-}1}$ or faster. While such a fast switching seems problematic for current AFM setups, the challenge remains open for future means to detect this dissipation by time-dependent magnetic fields, an electrostatic impurity level shift, or hybridization switching. The technical aspects revealed by this approach will be of interest for future nonequilibrium calculations.

DOI
10.1103/physrevb.107.035415

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The cyclic sudden switch of a magnetic impurity from a Kondo to a non-Kondo state and back was recently proposed to involve an important dissipation of the order of several kBTK{k}_{B}{T}_{K}kB​TK​ per cycle. The possibility to reveal this and other electronic processes through nanomechanical dissipation by, e.g., ultrasensitive atomic force microscope (AFM) tools would represent an unusual and interesting form of spectroscopy. Here, we explore the dependence on the switching time of the expected dissipation, a quantity whose magnitude is physically expected to drop from maximum to zero between sudden and slow switching, respectively. As an application of a recently established matrix-product-state-based time-dependent variational algorithm, we study the magnetic-field-induced Kondo switching in an Anderson model of the magnetic impurity. We find, quite reasonably, that dissipation requires switching within the Kondo timescale \ensuremathℏ(kBTK)\ensuremath−1\ensuremath{\hbar}{({k}_{B}{T}_{K})}^{\ensuremath{-}1}\ensuremathℏ(kB​TK​)\ensuremath−1 or faster. While such a fast switching seems problematic for current AFM setups, the challenge remains open for future means to detect this dissipation by time-dependent magnetic fields, an electrostatic impurity level shift, or hybridization switching. The technical aspects revealed by this approach will be of interest for future nonequilibrium calculations.
Understanding the time evolution of strongly correlated open quantum systems (OQSs) in response to perturbations (quenches) is of fundamental importance to the precise control of quantum devices. It is, however, rather challenging in multi-impurity quantum systems because such evolution often involves multiple intricate dynamical processes. In this work, we apply the numerically exact hierarchical equations of motion approach to explore the influence of two different types of perturbations, i.e., sudden swapping of the energy levels of impurity systems and activating the inter-impurity spin-exchange interaction, on the dissipation dynamics of the Kondo-correlated two-impurity Anderson model over a wide range of energetic parameters. By evaluating the time-dependent impurity spectral function and other system properties, we analyze the time evolution of the Kondo state in detail and conclude a phenomenologically scaling relation for Kondo dynamics driven by these perturbations. The evolutionary scaling relationship is not only related to the Kondo characteristic energy TK but also significantly affected by the simultaneous non-Kondo dynamic characteristic energy. We expect these results will inspire subsequent theoretical studies on the dynamics of strongly correlated OQSs.
We study the single-impurity Anderson model out of equilibrium under the influence of a bias voltage ϕ and a magnetic field B . We investigate the interplay between the shift ( ) of the Kondo peak in the spin-resolved density of states (DOS) and the one ( ) of the conductance anomaly. In agreement with experiments and previous theoretical calculations we find that, while the latter displays a rather linear behavior with an almost constant slope as a function of B down to the Kondo scale, the DOS shift first features a slower increase reaching the same behavior as only for . Our auxiliary master equation approach yields highly accurate nonequilibrium results for the DOS and for the conductance all the way from within the Kondo up to the charge fluctuation regime, showing excellent agreement with a recently introduced scheme based on a combination of numerical renormalization group with time-dependent density matrix renormalization group.
Single-particle dynamics of the Anderson impurity model in the presence of a magnetic field H are considered, using a recently developed local moment approach that encompasses all energy scales, field and interaction strengths. For strong coupling in particular, the Kondo scaling regime is recovered. Here the frequency (ω/ω K ) and field ( H /ω K ) dependence of the resultant universal scaling spectrum is obtained in large part analytically, and the field-induced destruction of the Kondo resonance investigated. The scaling spectrum is found to exhibit the slow logarithmic tails recently shown to dominate the zero-field scaling spectrum. At the opposite extreme of the Fermi level, it gives asymptotically exact agreement with results for statics known from the Bethe ansatz. Good agreement is also found with the frequency and field-dependence of recent numerical renormalization group calculations. Differential conductance experiments on quantum dots in the presence of a magnetic field are likewise considered, and appear to be well accounted for by the theory. Some new exact results for the problem are also established.
We study the nonequilibrium dynamics of a periodically driven anisotropic Kondo impurity model. The periodic time dependence is introduced for a local magnetic field which couples to the impurity spin and also for an in-plane exchange interaction. We obtain the exact results on the time evolution for arbitrary periodic time dependence at the special point in the parameter space known as the Toulouse limit. We first consider a specific case where the local magnetic field is periodically switched on and off. When the driving period is much shorter than the inverse of the Kondo temperature, an intriguing oscillating behavior (resonance phenomenon) emerges in the time average of the impurity spin polarization with increasing the local magnetic field intensity. By taking the high-frequency limit of the external driving, we elucidate that the system recovers the translational invariance in time and can be described by a mixture of the zero-temperature and infinite-temperature properties. In certain cases, the system is governed by either zero-temperature or infinite-temperature properties and, therefore, can be properly described by the corresponding equilibrium state.
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.
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.