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

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.

Figures (8)

• Figure 1: The different approximations to the FRG equations investigated in this work. The most elaborate scheme (FRG) truncates the flow equations at second order and separates the channels (no inter-channel mixing). The second scheme (rsFRG) reduces the numerical effort by an order of magnitude by only evaluating quantities on a discrete frequency grid of multiples of $\Omega/2$, the replica grid. In between, the quantities are linearly interpolated. Here, $n_f^{(2)}$ defines the maximal Floquet coefficient kept in all flowing quantities. The last and least computationally intensive scheme approximates all quantities as fully static in $\omega$ (sFRG).
• Figure 2: Renormalization of the time-averaged effective interaction $V$ and the $n=1$ component of the dot level $\varepsilon_{1}$ as a function of $1/\Delta$. As comparison, 2PT and GW results are shown. For the FRG, the three different approximations summarized in Fig. \ref{['fig:FRG approximation table']} are shown with solid, dashed and dotted lines respectively. The sFRG simulation diverges for $1/\Delta\approx \pi$ as in the equilibrium case.
• Figure 3: Self-energy and spectral function of the back-gate driven SIAM for different parameters. 2PT, GW, and frequency-dependent FRG results are shown. Panels (a)-(c) show the imaginary part of the time-averaged self-energy. It is negative in all drive-scenarios, i.e., preserves causality. Panels (d)-(f) show the time-averaged spectral function. It is strictly positive for all parameters and can indeed be interpreted as a spectral function. The reservoir temperature is given in units of $\Delta$ as $T_{\mathrm{res}}=0.01\Delta,\; 0.04\Delta,\; 0.06\Delta$ in (a),(d), (b),(e), and (c),(f) respectively.
• Figure 4: Floquet engineered effective mass by driving the back gate voltage in the SIAM. 2PT, GW and frequency dependent FRG are shown for small ($A/\Delta=0.5$) and large ($A/\Delta=5.0$) drive amplitude. The frequency is set to $\Omega/\Delta=5.0$, which is an intermediate to high drive frequency. The grey dash-dotted line marks the analytically known result for the equilibrium system Zlatic_1983. The reservoir temperature is $T_{\mathrm{res}}=0.05\Delta$, which is still below the Kondo temperature for the shown interaction strengths.
• Figure 5: Time averaged linear conductance as a function of gate voltage $V_g$ for different interaction strengths at $A /\Delta = \Omega/\Delta=5.0$. The black dashed line marks the position of the first Floquet replica peak in the noninteracting system at $V_g=\Omega$. The green dashed line marks the position of the Floquet replica of the Hubbard band located at $V_g=\Omega + U/2$. The reservoir temperature is set to $T_{\mathrm{res}}=0.05\Delta$.