Impact of nonlocal correlations over different energy scales: A Dynamical Vertex Approximation study

TL;DR

This study uses the dynamical vertex approximation to analyze how nonlocal correlations influence the physics of correlated electrons across different energy scales in the Hubbard model, revealing a smooth evolution from Slater to Heisenberg antiferromagnetic regimes.

Contribution

It applies the dynamical vertex approximation to characterize the energy-dependent effects of nonlocal correlations in the Hubbard model, bridging low-energy quasiparticle behavior and broader energy range properties.

Findings

Nonlocal correlations destroy Fermi-liquid behavior progressively.

Kinetic energy varies with interaction strength, indicating a transition from Slater to Heisenberg antiferromagnetism.

Potential energy analysis suggests improvements for ladder-based algorithms in DΓA.

Abstract

In this paper, we investigate how nonlocal correlations affect, selectively, the physics of correlated electrons over different energy scales, from the Fermi level to the band-edges. This goal is achieved by applying a diagrammatic extension of dynamical mean field theory (DMFT), the dynamical vertex approximation (D$\Gamma$A), to study several spectral and thermodynamic properties of the unfrustrated Hubbard model in two and three dimensions. Specifically, we focus first on the low-energy regime by computing the electronic scattering rate and the quasiparticle mass renormalization for decreasing temperatures at a fixed interaction strength. This way, we obtain a precise characterization of the several steps, through which the Fermi-liquid physics is progressively destroyed by nonlocal correlations. Our study is then extended to a broader energy range, by analyzing the temperature behavior of the kinetic and potential energy, as well as of the corresponding energy distribution functions. Our findings allow us to identify a smooth, but definite evolution of the nature of nonlocal correlations by increasing interaction: They either increase or decrease the kinetic energy w.r.t. DMFT depending on the interaction strength being weak or strong, respectively. This reflects the corresponding evolution of the ground state from a nesting-driven (Slater) to a superexchange-driven (Heisenberg) antiferromagnet (AF), whose fingerprints are, thus, recognizable in the spatial correlations of the paramagnetic phase. Finally, a critical analysis of our numerical results of the potential energy at the largest interaction allows us to identify possible procedures to improve the ladder-based algorithms adopted in the dynamical vertex approximation.