Exact low-temperature properties of a class of highly frustrated Hubbard models

TL;DR

This paper analytically and numerically investigates the low-temperature properties of a class of highly frustrated Hubbard models, revealing conditions for ferromagnetism and providing exact ground state solutions.

Contribution

It introduces exact solutions for many-electron ground states and thermodynamic quantities in frustrated Hubbard models, highlighting the role of electron density and interaction strength.

Findings

Saturated ferromagnetism occurs only at high electron densities and large U.

Exact ground states are constructed for a wide range of densities.

Low-temperature thermodynamic properties are derived in closed form.

Abstract

We study the repulsive Hubbard model both analytically and numerically on a family of highly frustrated lattices which have one-electron states localized on isolated trapping cells. We construct and count exact many-electron ground states for a wide range of electron densities and obtain closed-form expressions for the low-temperature thermodynamic quantities. Furthermore, we find that saturated ferromagnetism is obtained only for sufficiently high electron densities and large Hubbard repulsion $U$ while there is no finite average moment in the ground states at lower densities.