Metallic ferromagnetism in the Hubbard model: A rigorous example

Abstract

We present the first rigorous example of the Hubbard model in any dimensions which exhibits metallic ferromagnetism. The model is a genuine Hubbard model with short-range hopping and on-site Coulomb repulsion, and has multi single-electron bands. In the limit where the band gap and the Coulomb repulsion become infinite, we prove that the ground states are completely ferromagnetic and at the same time conducting.

4 pages, 2 figues. Minor improvements have been made. This version will appear in Phys. Rev. Lett

References in corpus (4)

• Stability of ferromagnetism in the Hubbard model on the kagomé lattice
• Stability of Ferromagnetism in Hubbard Models with Nearly-Flat Bands
• Ferromagnetism in the Hubbard model: A constructive approach
• An extension of Tasaki's flat-band Hubbard model

Cited by in corpus (27)

• Itinerant Ferromagnetism in a Fermi Gas of Ultracold Atoms
• Competition between pairing and ferromagnetic instabilities in ultracold Fermi gases near Feshbach resonances
• Stability of a Fully Magnetized Ferromagnetic state in Repulsively Interacting Ultracold Fermi Gases
• Low-temperature properties of the Hubbard model on highly frustrated one-dimensional lattices
• One-dimensional sawtooth and zigzag lattices for ultracold atoms
• Correlated versus Ferromagnetic State in Repulsively Interacting Two-Component Fermi Gases
• Spintronics at Nanoscale: Flat-Band Ferromagnetism in Armchair Nanoribbons and Nanotubes
• Ferromagnetism in armchair graphene nanoribbon
• Exact Results on Itinerant Ferromagnetism in Multi-orbital Systems on Square and Cubic Lattices
• Ferromagnetism and its stability from the one-magnon spectrum in twisted bilayer graphene
• Interacting spinless fermions in a diamond chain
• Low-temperature thermodynamics for a flat-band ferromagnet: Rigorous versus numerical results
• Statistical Mechanics and the Physics of the Many-Particle Model Systems
• Molecular-orbital representation of generic flat-band models
• Conductance through geometrically frustrated itinerant electronic systems
• Itinerant Ferromagnetism and $p+i{p}^{\prime }$ Superconductivity in Doped Bilayer Silicene
• Dispersion-driven ferromagnetism in a flat-band Hubbard system
• An extension of the cell-construction method for the flat-band ferromagnetism
• The Pauli principle and magnetism
• Exact results for itinerant ferromagnetism in a $t_{2g}$ orbital system on cubic and square lattices
• Construction of interacting flat-band models by molecular-orbital representation: Correlation functions, energy gap, and entanglement
• Metallic ferromagnetism supported by a single band in a multi-band Hubbard model
• Ferromagnetism in the Hubbard model with a gapless nearly-flat band
• Ferromagnetic Pairing States on Two-Coupled Chains
• Stability of the Nagaoka-type Ferromagnetic State in a $t_{2g}$ Orbital System on a Cubic Lattice
• Quadratic operators used in deducing exact ground states for correlated systems: ferromagnetism at half filling provided by a dispersive band
• Kondo dynamics in one-dimensional doped ferromagnetic insulators