Hubbard-like Hamiltonians for interacting electrons in s, p and d orbitals

TL;DR

This paper derives the most general Hubbard-like Hamiltonians for s, p, and d orbitals consistent with symmetries and compares their effectiveness to simpler models in describing electron interactions in strongly-correlated solids.

Contribution

It provides a comprehensive derivation of the general form of Hubbard-like Hamiltonians for p and d orbitals, clarifying their structure and practical implementation.

Findings

Correct Hamiltonians better describe ground states and excited state dynamics.

Stoner Hamiltonians can misrepresent electronic heat capacity.

Full configuration interaction highlights differences between models.

Abstract

Hubbard-like Hamiltonians are widely used to describe on-site Coulomb interactions in magnetic and strongly-correlated solids, but there is much confusion in the literature about the form these Hamiltonians should take for shells of p and d orbitals. This paper derives the most general s, p and d orbital Hubbard-like Hamiltonians consistent with the relevant symmetries, and presents them in ways convenient for practical calculations. We use the full configuration interaction method to study p and d orbital dimers and compare results obtained using the correct Hamiltonian and the collinear and vector Stoner Hamiltonians. The Stoner Hamiltonians can fail to describe properly the nature of the ground state, the time evolution of excited states, and the electronic heat capacity.