We identify the precise hallmarks of the local magnetic moment formation and its Kondo screening in the frequency structure of the generalized charge susceptibility. The sharpness of our identification even pinpoints an alternative criterion to determine the Kondo temperature of strongly correlated systems on the two-particle level, which only requires calculations at the lowest Matsubara frequency. We showcase its strength by applying it to the single impurity and the periodic Anderson model as well as to the Hubbard model. Our results represent a significant progress for the general understanding of quantum field theory at the two-particle level and allow for tracing the limits of the physics captured by perturbative approaches for correlated systems.
The Kondo and periodic Anderson models describe many of the qualitative features of local moments coupled to a conduction band, and thereby the physics of materials such as the heavy fermions. In particular, when the exchange coupling
J or hybridization
V between the moments and the electrons of the metallic band is large, singlets form, quenching the magnetism. In the opposite, small
J or
V, limit, the moments survive and the conduction electrons mediate an effective interaction which can trigger long-range, often antiferromagnetic order. In the case of the Kondo model, where the moments are described by local spins, Nozi\`eres considered the possibility that the available conduction electrons within the Kondo temperature of the Fermi surface would be insufficient in number to accomplish the screening. Much effort in the literature has been devoted to the study of the temperature scales in the resulting ``exhaustion'' problem and how the ``coherence temperature'' where a heavy Fermi liquid forms is related to the Kondo temperature. In this paper, we study a version of the periodic Anderson model in which some of the conduction electrons are removed in a way which avoids the fermion sign problem and hence allows low-temperature quantum Monte Carlo simulations which can access both singlet formation and magnetic ordering temperature scales. We are then able to focus on a somewhat different aspect of exhaustion physics than previously considered: the effect of dilution on the critical
V for the singlet-antiferromagnetic transition.
We study the formation of local magnetic moments in the strongly correlated Hubbard model within dynamical mean-field theory and associate peculiarities of the temperature dependence of local charge ${\ensuremath{\chi}}_{c}$ and spin ${\ensuremath{\chi}}_{s}$ susceptibilities with different stages of local moment formation. The local maximum of the temperature dependence of the charge susceptibility ${\ensuremath{\chi}}_{c}$ is associated with the beginning of local magnetic moment formation, while the minimum of the susceptibility ${\ensuremath{\chi}}_{c}$ and double occupation, as well as the low-temperature boundary of the plateau of the effective local magnetic moment ${\ensuremath{\mu}}_{\mathrm{eff}}^{2}=T{\ensuremath{\chi}}_{s}$ temperature dependence are connected with the full formation of local moments. We also obtain the interaction dependence of the Kondo temperature
TK, which is compared to the fingerprint criterion of Chalupa et al. [Phys. Rev. Lett. 126, 056403 (2021)]. Near the Mott transition the two criteria coincide, while further away from the Mott transition the fingerprint criterion somewhat overestimates the Kondo temperature. The relation of the observed features to the behavior of eigenvectors/eigenvalues of fermionic frequency-resolved charge susceptibility and divergences of irreducible vertices is discussed.