Topological frustration and structural balance in strongly correlated itinerant electron systems: an extension of Nagaoka's theorem

Abstract

We prove that Nagaoka's theorem, that the large-$U$ Hubbard model with exactly one hole is ferromagnetic, holds for any balanced Hamiltonian. Simply put, if a positive bond encodes friendship and a negative bond encodes enmity, then balance implies when that enemy of one's enemy is one's friend. We argue that, in itinerant electron systems, a balanced Hamiltonian, rather than bipartite lattice, defines an unfrustrated system. The proof is valid for multi-orbital models with arbitrary two-orbital interactions provided that no exchange interactions are antiferromagnetic: a class of models including the Kanomori Hamiltonian.

5 pages, 2 figures

References in corpus (3)

• Quantum frustration in organic Mott insulators: from spin liquids to unconventional superconductors
• Evolution of Nagaoka phase with kinetic energy frustrating hoppings
• Tuning Kinetic Magnetism of Strongly Correlated Electrons via Staggered Flux

Cited by in corpus (2)

• Kinetic magnetism in the crossover between the square and triangular lattice Fermi-Hubbard models
• Shaping Magnetic Order by Local Frustration for Itinerant Fermions on a Graph