Zero-frequency response functions and correlation functions in the Kondo and Anderson models /

S.C. Bradley, R. Bulla, A.C. Hewson +1 more

N. S. Maslova, P. I. Arseyev, Vladimir N. Mantsevich

Niaz Ali Khan

Zakaria M. M. Mahmoud, Florian Gebhard

We study the non‐interacting single‐impurity Anderson model (resonant level model) on a lattice at finite temperature as an illustrative example for an exactly solvable quantum‐mechanical problem, and derive the free energy, various thermodynamic potentials (internal energy, entropy, magnetization), and response functions (specific heat, zero‐field magnetic susceptibility). We calculate the magnetic screening cloud, and derive the corresponding correlation length in one dimension beyond which the correlations decay exponentially. The present results remain qualitatively applicable for the interacting single‐impurity Anderson model when the energy scale Г of the resonant‐level model is replaced by the Kondo scale TK.

S. C. BRADLEY, R. Bulla, Alex C. Hewson +1 more

The O(3) symmetric Anderson model is an example of a system which has a stable low energy marginal Fermi liquid fixed point for a certain choice of parameters. It is also exactly equivalent, in the large U limit, to a localized model which describes the spin degrees of freedom of the linear dispersion two channel Kondo model. We first use an argument based on conformal field theory to establish this precise equivalence with the two channel model. We then use the numerical renormalization group (NRG) approach to calculate both one-electron and two-electron response functions for a range of values of the interaction strength U. We compare the behaviours about the marginal Fermi liquid and Fermi liquid fixed points and interpret the results in terms of a renormalized Majorana fermion picture of the elementary excitations. In the marginal Fermi liquid case the spectral densities of all the Majorana fermion modes display a |omega| dependence on the lowest energy scale, and in addition the zero Majorana mode has a delta function contribution. The weight of this delta function is studied as a function of the interaction U and is found to decrease exponentially with U for large U. Using the equivalence with the two channel Kondo model in the large U limit, we deduce the dynamical spin susceptibility of the two channel Kondo model over the full frequency range. We use renormalized perturbation theory to interpret the results and to calculate the coefficient of the ln omega divergence found in the low frequency behaviour of the T=0 dynamic susceptibility.

Jan-Niklas Herre, Christoph Karrasch, Dante Marvin Kennes

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.