Dynamics and scaling in the periodic Anderson model

TL;DR

This paper develops a non-perturbative local moment approach within dynamical mean-field theory to analyze the single-particle dynamics of the periodic Anderson model across all energy scales and interaction strengths, emphasizing universal scaling in the Kondo lattice regime.

Contribution

It introduces a comprehensive local moment approach that captures the full energy spectrum and interaction regimes of the periodic Anderson model, highlighting universal scaling behavior.

Findings

Universal scaling of dynamics as a function of b1=b1/b1_L in the Kondo lattice regime

Crossover from Fermi liquid to single-impurity physics at higher energies

Incompatibility with two-scale exhaustion physics

Abstract

The periodic Anderson model (PAM) captures the essential physics of heavy fermion materials. Yet even for the paramagnetic metallic phase, a practicable many-body theory that can simultaneously handle all energy scales while respecting the dictates of Fermi liquid theory at low energies, and all interaction strengths from the strongly correlated Kondo lattice through to weak coupling, has remained quite elusive. Aspects of this problem are considered in the present paper where a non-perturbative local moment approach (LMA) to single-particle dynamics of the asymmetric PAM is developed within the general framework of dynamical mean-field theory. All interaction strengths and energy scales are encompassed, although our natural focus is the Kondo lattice regime of essentially localized $f$-spins but general conduction band filling, characterised by an exponentially small lattice coherence scale $\omega_{L}$. Particular emphasis is given to the resultant universal scaling behaviour of dynamics in the Kondo lattice regime as an entire function of $\omega^{\prime} =\omega/\omega_{L}$, including its dependence on conduction band filling, $f$-level asymmetry and lattice type.A rich description arises, encompassing both coherent Fermi liquid behaviour at low-$\omega^{\prime}$ and the crossover to effective single-impurity scaling physics at higher energies -- but still in the $\omega/\omega_{L}$-scaling regime, and as such incompatible with the presence of two-scale `exhaustion' physics, which is likewise discussed.