Universal Signature of Hundness and Its Quantification

Abstract

Hund's coupling $J$ induces fundamentally different correlation effects from Hubbard $U$. This leads to a violation of the Brinkman--Rice scenario and the emergence of a Janus-faced phase owing to its low-energy effectiveness, in which band renormalization is confined below a characteristic energy scale. We propose a quantitative framework to capture low-energy effectiveness through two correlation factors: $z_L$ for low-energy quasiparticle renormalization and $z_H$ for high-energy charge fluctuations, newly introduced in this study. The discrepancy between $z_L$ and $z_H$ reflects the Hund character of the correlation. By establishing a one-to-one correspondence between correlation factors and the spin and charge susceptibilities, we identify the spin-degree-of-freedom effectiveness as the microscopic origin of low-energy effectiveness. Our framework, validated across multiorbital models and real materials, provides a universal and quantitative measure of Hundness.