The Hubbard model extended by nearest-neighbor Coulomb and exchange interaction on a cubic cluster - rigorous and exact results

TL;DR

This paper provides a comprehensive, exact analysis of an extended Hubbard model on a cubic cluster, including Coulomb and exchange interactions, revealing detailed ground state properties, degeneracies, and thermodynamics across all parameters.

Contribution

It offers the first complete eigensystem solutions for all electron numbers and parameters, including analytical results for specific cases and detailed exploration of degeneracies and phase behavior.

Findings

Exact eigensystem for all electron occupancies and parameters.

Identification of ground state level crossings and degeneracy lines.

Analysis of spin correlations and thermodynamic properties.

Abstract

The Hubbard model on a cube was revisited and extended by both nearest-neighbor (nn) Coulomb correlation and {nearest-neighbor} Heisenberg exchange. The complete eigensystem was computed exactly for all electron occupancies and all model parameters ranging from minus infinity to plus infinity. For two electrons on the cluster the eigensystem is given in analytical form. For six electrons and infinite on-site correlation U we determinded the groundstate and the groundstate energy of the pure Hubbard model analytically. For fixed electron numbers we found a multitude of ground state level crossings in dependence on the various model parameters. Furthermore the groundstates of the pure Hubbard model in dependence on a magnetic field h coupled to the spins are shown for the complete U-h plane. For the cubic cluster gas we calculated the density $n(\mu,T,h)$ and the thermodynamical density of states from the grand potential. The ground states and the various spin-spin correlation functions are studied for both attractive and repulsive values of the three interaction constants. The anomalous degeneration lines are calculated. For the cases where these lines end in triple points we give the related parameter values. The influence of the nn-exchange and the nn-Coulomb correlation onto the anomalous degeneration is discussed.