Dynamical Mean-Field Theory Plus Numerical Renormalization-Group Study of Spin-Orbital Separation in a Three-Band Hund Metal

TLDR

The study demonstrates that the numerical renormalization group can serve as a multi‑band impurity solver for DMFT, delivering unprecedented real‑frequency spectral resolution at very low energies and temperatures. The authors apply the NRG‑based DMFT to a three‑band Hund metal on a Bethe lattice at one‑third filling, yielding a numerically exact solution. The exact DMFT solution reveals a Fermi‑liquid ground state that undergoes a coherence‑incoherence crossover with temperature, exhibits strong particle‑hole asymmetry, shows power‑law self‑energy behavior only for positive frequencies, and displays spin‑orbital separation where spin screening occurs at lower energies than orbital screening, with renormalization‑group flows capturing the physics across all scales.

Abstract

We show that the numerical renormalization group is a viable multi-band impurity solver for dynamical mean-field theory (DMFT), offering unprecedented real-frequency spectral resolution at arbitrarily low energies and temperatures. We use it to obtain a numerically exact DMFT solution to the Hund metal problem for a three-band model on a Bethe lattice at 1/3 filling. The ground state is a Fermi liquid. The one-particle spectral function undergoes a coherence-incoherence crossover with increasing temperature, with spectral weight being transferred from low to high energies. Further, it exhibits a strong particle-hole asymmetry. In the incoherent regime, the self-energy displays approximate power-law behavior for positive frequencies only. The spin and orbital spectral functions show "spin-orbital separation": spin screening occurs at much lower energies than orbital screening. The renormalization group flows clearly reveal the relevant physics at all energy scales.