Hund-projected Kanamori model: an effective description of Hund's metals near the Mott insulating regime

TL;DR

This work derives a Hund-projected Kanamori model (HPKM) by projecting the multi-orbital Hubbard-Kanamori Hamiltonian onto the high-spin manifold favored by Hund's coupling, establishing a rigorous low-energy description for doped Hund's metals near the Mott regime. In the undoped limit, the HPKM reduces to a spin-$N/2$ Heisenberg system with suppressed quantum fluctuations, while doping activates a Hund-enhanced kinetic mechanism that drives strong ferromagnetic correlations, akin to, but far more potent than, Nagaoka ferromagnetism. The framework yields a computationally tractable platform with a reduced sign problem, enabling advanced path-integral and diagrammatic methods to access quasiparticle structure and carrier interactions beyond DMFT. Overall, the HPKM provides a microscopic bridge between Kanamori physics and the emergent magnetic and transport phenomena characteristic of Hund's metals, illuminating how spin, charge motion, and Hund's coupling co-determine metallicity near Mott insulating states.

Abstract

Hund's coupling plays a decisive role in shaping electron correlations of multi-orbital systems, giving rise to a class of materials--Hund's metals--that combine local-moment physics with metallic transport. Here we derive an effective low-energy description of such a system near the Mott insulating regime, starting from the multi-orbital Hubbard-Kanamori Hamiltonian and projecting onto the high-spin manifold favored by Hund's first rule. The resulting Hund-projected Kanamori model captures the interplay between carrier motion and magnetic correlations in the presence of strong Hund's coupling. In the undoped limit, the model reduces to a spin-$N/2$ Heisenberg system with suppressed quantum fluctuations, approaching the classical limit for realistic five-band configurations. Upon doping, carrier motion couples strongly to the spin background and drives ferromagnetic correlations through a Hund-enhanced kinetic mechanism analogous to, but much stronger than, Nagaoka ferromagnetism. Owing to its reduced sign problem, the model can be addressed with advanced path-integral methods to determine quasiparticle structure and effective interactions between carriers-quantities that are challenging to obtain with other methods. This framework establishes a microscopic bridge between the Kanamori model and the emergent magnetic and transport phenomena characteristic of Hund's metals.