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arXiv:2603.12844 · Physical review. B./Physical review. B

Many-body correlations in Floquet steady states: Frequency-resolved renormalization group of the driven Anderson impurity

Jan-Niklas Herre, Christoph Karrasch, Dante Marvin Kennes

Published Jun 16, 2026• 0 citations
arXivHTMLPDF

Abstract

We introduce a functional renormalization group framework formulated directly in the Floquet steady state that systematically incorporates frequency-dependent interaction effects. By retaining the frequency structure of the two-particle vertex up to second order in interaction strength, our approach provides controlled access to dynamical response functions and nonequilibrium transport in driven, interacting systems. Using the periodically driven single-impurity Anderson model as a paradigmatic example, we benchmark our results against state-of-the-art Floquet Green's function methods and find quantitative agreement for finite-frequency observables up to intermediate interaction strengths. Remarkably, we also show that static properties are often captured reliably by much simpler approximations, suggesting practical pathways for modeling driven quantum materials. Finally, we demonstrate that although periodic driving of the dot strongly broadens the Kondo resonance through inelastic scattering, it leaves the many-body Kondo cloud largely intact. This robustness suppresses Floquet replicas of the Kondo peak and leads to a partial persistence of Kondo pinning, highlighting the resilience of emergent many-body correlations under local periodic driving.

DOI
10.1103/693m-tklt

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We introduce a functional renormalization group framework formulated directly in the Floquet steady state that systematically incorporates frequency-dependent interaction effects. By retaining the frequency structure of the two-particle vertex up to second order in interaction strength, our approach provides controlled access to dynamical response functions and nonequilibrium transport in driven, interacting systems. Using the periodically driven single-impurity Anderson model as a paradigmatic example, we benchmark our results against state-of-the-art Floquet Green's function methods and find quantitative agreement for finite-frequency observables up to intermediate interaction strengths. Remarkably, we also show that static properties are often captured reliably by much simpler approximations, suggesting practical pathways for modeling driven quantum materials. Finally, we demonstrate that although periodic driving of the dot strongly broadens the Kondo resonance through inelastic scattering, it leaves the many-body Kondo cloud largely intact. This robustness suppresses Floquet replicas of the Kondo peak and leads to a partial persistence of Kondo pinning, highlighting the resilience of emergent many-body correlations under local periodic driving.
We study the interplay of strong correlations and coherent driving by considering the strong coupling Kondo model driven by a time-periodic bias voltage. Combining a recent nonequilibrium renormalization group method with Floquet theory, we find that by the coherent dressing of the driving field side replicas of the Kondo resonance emerge in the conductance, which are not completely washed out by the decoherence induced by the driving. We show that to accurately capture the interplay of driving and strong correlations one needs to go beyond simple phenomenological pictures, which underestimate decoherence, or adiabatic approximations, highlighting the relevance of non-Markovian memory effects. Within our method the differential conductance shows good quantitative agreement with experimental data in the full crossover regime from weak to strong driving. We analyze memory effects in detail based on the response to short voltage pulses.
The main goal of the present thesis is to set up a functional renormalization group formalism in Floquet space to treat interacting, time periodic quantum dots and to investigate the consequential renormalization of the parameters and the transport through the dot. Building upon the time independent, steady state description in frequency space (Karrasch 2010, Jakobs 2009) and a time dependent FRG formulation (Kennes 2014), we tackle the steady state of periodically driven quantum dots. We focus on the long time behavior where all transients have died out, and therefore the entire system is characterized by the same periodicity as given by the driven external fields. As a consequence, we can transform the according time dependent flow equation to Floquet space using Floquet-Green’s functions. It allows us to study quantum dot systems in the whole range of driving frequency and amplitude in the presence of a small Coulomb interaction. We exemplify the potential of our approach by applying it to the interacting resonant level model (IRLM), describing an idealized single level quantum dot dominated only by charge fluctuations.We investigate the role of the driving frequency Ω in the RG flows of the time periodic parameters of the IRLM. The small driving amplitude limit allows to complement our numerical solution by analytic expressions of the renormalization of all dot parameters to the leading order of driving amplitude over mean value. Four different configurations are studied, where distinct combinations of the hopping and/or onsite energy of the dot are chosen to be time periodic. The transparent structure of the renormalization of the parameters in this limit, allows for an analytic treatment of all higher harmonics, where the various protocols reveal very different RG flows. Even beyond the small driving amplitude limit the RG flow is discussed with the help of an effective reservoir distribution function which can be defined in this setup and its form is defined by the ratio of driving amplitude and frequency (Suzuki 2015). The second focus is directed to the transport in the time periodic quantum dot systems and how it is affected by the Coulomb interaction. Based on the well studied parameter pump in the adiabatic limit (Brouwer 1998), where two parameters are varied periodically and phase shifted, we like to investigate the pumped charge in the whole regime of driving frequency and amplitude including interaction in such a setup. Further a single parameter pump is realized and the charge susceptibility as well as the mean current are studied. The latter reveals power law behavior on the driving frequency. A quantum master equation calculation in Floquet-Liouville space complements the FRG results to study the requirements of such a single parameter quantum pump. Finally, the conductance and the current are considered for several time periodic hoppings of non-sinusoidal form.
Periodically driven quantum systems provide a powerful route to engineer novel states of matter by controlling their effective Hamiltonians through external fields. However, most treatments are usually simplified by considering the high-frequency limit, and do not account for the processes taking place in the transient regime during the onset of the drive. In this work, we introduce a time and momentum resolved tunneling spectroscopy protocol to probe the instantaneous energy spectrum of Floquet-driven systems beyond the high-frequency regime, capturing both emergent effects and non-adiabatic phenomena without requiring explicit reconstruction of the full time-dependent Green's function. We benchmark the method on driven non-interacting fermionic models, and then generalize the approach to strongly correlated systems with the aid of time-dependent density matrix renormalization group techniques. We also provide a microscopic description to the emergence of in-gap states under resonant driving, and briefly explore its finite temperature analog.
We present an extension of the functional renormalization group to Floquet space, which enables us to treat the long time behavior of interacting time periodically driven quantum dots. It is one of its strength that the method is neither bound to small driving amplitudes nor to small driving frequencies, i.e., very general time periodic signals can be considered. It is applied to the interacting resonant level model, a prototype model of a spinless, fermionic quantum dot. The renormalization in several setups with different combinations of time periodic parameters is studied, where the numerical results are complemented by analytic expressions for the renormalization in the limit of small driving amplitude. We show how the driving frequency acts as an infrared cutoff of the underlying renormalization group flow which manifests in novel power laws. We utilize the tunability of the effective reservoir distribution function in a periodically driven onsite energy setup to show how its shape is directly reflected in the renormalization group flow. This allows us to flexibly tune the power-law renormalization generically encountered in quantum dot structures. Finally, an in-phase quantum pump as well as a single parameter pump are investigated in the whole regime of driving frequency, demonstrating that the new power law in the driving frequency is reflected in the mean current of the latter.
We investigate nonequilibrium properties of the single-impurity Anderson model by means of the functional renormalization group (fRG) within Keldysh formalism. We present how the level broadening $\ensuremath{\Gamma}/2$ can be used as flow parameter for the fRG. This choice preserves important aspects of the Fermi-liquid behavior that the model exhibits in case of particle-hole symmetry. An approximation scheme for the Keldysh fRG is developed which accounts for the frequency dependence of the two-particle vertex in a way similar but not equivalent to a recently published approximation to the equilibrium Matsubara fRG. Our method turns out to be a flexible tool for the study of weak to intermediate on-site interactions $U\ensuremath{\lesssim}3\ensuremath{\Gamma}$. In equilibrium we find excellent agreement with numerical RG results for the linear conductance at finite gate voltage, magnetic field, and temperature. In nonequilibrium, our results for the current agree well with time-dependent density-matrix RG. For the nonlinear conductance as function of the bias voltage, we propose reliable results at finite magnetic field and finite temperature. Furthermore, we demonstrate the exponentially small scale of the Kondo temperature to appear in the second-order derivative of the self-energy. We show that the approximation is, however, not able to reproduce the scaling of the effective mass at large interactions.
Driving a quantum system periodically in time can profoundly alter its long-time correlations and give rise to exotic quantum states of matter. The complexity of the combination of many-body correlations and dynamic manipulations has the potential to uncover a whole field of new phenomena, but the theoretical and numerical understanding becomes extremely difficult. We now propose a promising numerical method by generalizing the density matrix renormalization group to a superposition of Fourier components of periodically driven many-body systems using Floquet theory. With this method we can study the full time-dependent quantum solution in a large parameter range for all evolution times, beyond the commonly used high-frequency approximations. Numerical results are presented for the isotropic Heisenberg antiferromagnetic spin-1/2 chain under both local(edge) and global driving for spin-spin correlations and temporal fluctuations. As the frequency is lowered, we demonstrate that more and more Fourier components become relevant and determine strong length- and frequency-dependent changes of the quantum correlations that cannot be described by effective static models.