The Hubbard model on a complete graph: exact analytical results

The Hubbard Model on a Complete Graph: Exact Analytical Results

We derive the analytical expression of the ground state of the Hubbard model with unconstrained hopping at half filling and for arbitrary lattice sites. PACS: 03.65.Ge, 03.70.+k, 11.10.Lm Istituto Nazionale per la Fisica della Materia and Department of Theoretical Physics, University of Salerno, 84100 Salerno, Italy. Email:[email protected]

The Erwin Schrr Odinger International Institute for Mathematical Physics the Hubbard Model on a Complete Graph: Exact Analytical Results

Antiferromagnetism in the Exact Ground State of the Half Filled Hubbard Model on the Complete-Bipartite Graph

As a prototype model of antiferromagnetism, we propose a repulsive Hubbard Hamiltonian defined on a graph Λ = A∪B with A∩B = ∅ and bonds connecting any element of A with all the elements of B. Since all the hopping matrix elements associated with each bond are equal, the model is invariant under an arbitrary permutation of the A-sites and/or of the B-sites. This is the Hubbard model defined on ...

A Note on Ferromagnetism in the Hubbard Model on the Complete Graph

Recently there have appeared some papers which discuss the existence of ferromagnetism in the Hubbard model defined on the complete graph. At least for the special electron number Ne = N − 1, where N denotes the number of sites in the lattice, the existence of ferromagnetism in this model was established rigorously some time ago, as special (and indeed the simplest) cases of more general classe...

Ferromagnetic ground states of the Hubbard model on a complete graph

We use group theory to derive the exact analytical expression of the ferromagnetic ground states of the Hubbard model on a complete graph for arbitrary lattice sites f and for arbitrary fillings N . We find that for t > 0 and for N = f + 1 the ground state is maximally ferromagnetic with total spin S = (f − 1)/2. For N > f + 1 the ground state is still ferromagnetic but becomes degenerate with ...