Exact ferromagnetic ground state of pentagon chains

TL;DR

This paper proves the existence of exact ferromagnetic ground states in conducting pentagon chains modeled by a multi orbital Hubbard model, using a positive semidefinite transformation technique that is broadly applicable.

Contribution

It introduces a rigorous method to establish ferromagnetism in pentagon chains without relying on model integrability or specific dimensional constraints.

Findings

Exact ferromagnetic ground states are proven to exist below half filling.

The ferromagnetism is linked to dispersionless bands but does not require flat band conditions.

Only a small, possibly random, subset of sites need to interact for ferromagnetism to occur.

Abstract

We model conducting pentagon chains with a multi orbital Hubbard model and prove that well below half filling exact ferromagnetic ground states appear. The rigorous method we use is based on the transformation of original hamiltonian into positive semidefinite form. This technique is independent of the spatial dimesion and does not require integrability of the model. The obtained ferromagnetism is connected to dispersionless bands but in a much broader sense than flat band ferromagnetism requires, where on every site a Hubbard term is present. In our case only a small percentage of, even randomly distributed, sites are only interacting.