Quadratic operators used in deducing exact ground states for correlated systems: ferromagnetism at half filling provided by a dispersive band

TL;DR

This paper introduces a method using quadratic operators to transform the Hamiltonian of a correlated dispersive band, enabling the derivation of exact ground states and demonstrating ferromagnetism at half filling due to correlation effects.

Contribution

It presents a novel approach to obtain exact ground states of correlated systems using quadratic operators, highlighting ferromagnetism in dispersive bands at half filling.

Findings

Quadratic operators can transform the Hamiltonian into a positive semidefinite form.

Exact ground states can be deduced for correlated dispersive bands.

Dispersive bands can exhibit ferromagnetism at half filling due to correlation effects.

Abstract

Quadratic operators are used in transforming the model Hamiltonian (H) of one correlated and dispersive band in an unique positive semidefinite form coopting both the kinetic and interacting part of H. The expression is used in deducing exact ground states which are minimum energy eigenstates only of the full Hamiltonian. It is shown in this frame that at half filling, also dispersive bands can provide ferromagnetism in exact terms by correlation effects .