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

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.

31 pages, 13 figures,2 tables. Main text at pages 1-17. Pages 18-31 contain the analytical solution for two electrons

References in corpus (16)

• Quantum Cluster Theories
• Electron transport through single Mn12 molecular magnets
• Tunable Non-local Spin Control in a Coupled Quantum Dot System
• Variational cluster approach to correlated electron systems in low dimensions
• Transition between Quantum States in a Parallel-Coupled Double-Quantum-Dot
• Magnetically Tunable Kondo - Aharonov-Bohm Effect in a Triangular Quantum Dot
• Superconductivity in Inhomogeneous Hubbard Models
• The Optimal Inhomogeneity for Superconductivity: Finite Size Studies
• Dynamical symmetry breaking in transport through molecules
• An exact study of charge-spin separation, pairing fluctuations and pseudogaps in four-site Hubbard clusters
• Nearest-Neighbor Repulsion and Competing Charge and Spin Order in the Extended Hubbard Model
• Mott transition in one dimension: Benchmarking dynamical cluster approaches
• Self-energy-functional theory for systems of interacting electrons with disorder
• Electron coherent and incoherent pairing instabilities in inhomogeneous bipartite and nonbipartite nanoclusters
• Analytical solution of a Hubbard model extended by nearest neighbour Coulomb and exchange interaction on a triangle and tetrahedron
• Rigorous solution of a Hubbard model extended by nearest-neighbor Coulomb and isotropic exchange interaction on a triangle and tetrahedron

Cited by in corpus (8)

• Hubbard pair cluster in the external fields. Studies of the chemical potential
• Exchange-correlation magnetic fields in spin-density-functional theory
• Quantum many-body states and Green functions of nonequilibrium electron-magnon systems: Localized spin operators vs. their mapping to Holstein-Primakoff bosons
• Magnetocaloric and electrocaloric properties of the Hubbard pair cluster
• Hubbard pair cluster in the external fields. Studies of the polarization and susceptibility
• Hubbard pair cluster in the external fields. Studies of the magnetic properties
• Hubbard pair cluster with elastic interactions. Studies of thermal expansion, magnetostriction and electrostriction
• Exact Diagonalization Study of an Extended Hubbard Model for a Cubic Cluster at Quarter Filling