Strongly correlated materials from a numerical renormalization group perspective: How the Fermi-liquid state of Sr$_2$RuO$_4$ emerges

TL;DR

This paper uses the numerical renormalization group to study the emergence of the Fermi-liquid state in Sr$_2$RuO$_4$, revealing a two-stage screening process and the influence of van Hove singularities on orbital differentiation.

Contribution

It demonstrates the viability of NRG for real-materials dynamical mean-field theory and uncovers detailed spin-orbital screening and interactions in Sr$_2$RuO$_4$.

Findings

Orbital fluctuations are screened at higher energies than spin fluctuations.

Fermi-liquid behavior appears below 25 K with spin coherence.

Van Hove singularity causes strong orbital differentiation.

Abstract

The crossover from fluctuating atomic constituents to a collective state as one lowers temperature or energy is at the heart of the dynamical mean-field theory description of the solid state. We demonstrate that the numerical renormalization group is a viable tool to monitor this crossover in a real-materials setting. The renormalization group flow from high to arbitrarily small energy scales clearly reveals the emergence of the Fermi-liquid state of Sr$_2$RuO$_4$. We find a two-stage screening process, where orbital fluctuations are screened at much higher energies than spin fluctuations, and Fermi-liquid behavior, concomitant with spin coherence, below a temperature of 25 K. By computing real-frequency correlation functions, we directly observe this spin--orbital scale separation and show that the van Hove singularity drives strong orbital differentiation. We extract quasiparticle interaction parameters from the low-energy spectrum and find an effective attraction in the spin-triplet sector.