Quantum-geometry-driven exact ferromagnetic ground state in a nearly flat band

TL;DR

This paper constructs a Hubbard model with a tunable quantum geometry in a nearly flat band, demonstrating that quantum geometry alone can induce and control ferromagnetism and magnetic phase transitions.

Contribution

It introduces a model where quantum geometry independently influences ferromagnetism, revealing its fundamental role in many-body magnetic phenomena without mean-field approximations.

Findings

Exact ferromagnetic ground state at half-filling

Quantum metric stabilizes ferromagnetism via spin stiffness

Quantum geometry tuning induces magnetic phase transition

Abstract

We construct a Hubbard model with a nearly flat band whose quantum geometry can be tuned independently of the energy dispersion and the Coulomb interaction. We show that, when the nearly flat band is half-filled, the exact ground state of the model exhibits ferromagnetism and that this ferromagnetism is stabilized by the quantum metric through the spin stiffness. Furthermore, we demonstrate that tuning the quantum geometry alone drives a magnetic phase transition. Our nonperturbative results without resorting to mean-field approximations reveal the quantum-geometric origin of ferromagnetism and the underlying many-body physics in dispersive-band systems.