Ground state energy of the low density Hubbard model. An upper bound

Abstract

We derive an upper bound on the ground state energy of the three-dimensional (3D) repulsive Hubbard model on the cubic lattice agreeing in the low density limit with the known asymptotic expression of the ground state energy of the dilute Fermi gas in the continuum. As a corollary, we prove an old conjecture on the low density behavior of the 3D Hubbard model, i.e., that the total spin of the ground state vanishes as the density goes to zero.

13 pages; Version accepted for publication on the Journal of Mathematical Physics; minor changes

References in corpus (3)

• Ground State Energy of the Low Density Bose Gas
• Ground State Energy of the Low Density Fermi Gas
• Ferromagnetism of the Hubbard Model at Strong Coupling in the Hartree-Fock Approximation

Cited by in corpus (5)

• Time Dependent Density Functional Theory meets Dynamical Mean Field Theory: Real-Time Dynamics for the 3D Hubbard model
• The 2D Hubbard model on the honeycomb lattice
• The dilute Fermi gas via Bogoliubov theory
• Ground state energy of the low density Hubbard model
• Ground state energy of the polarized diluted gas of interacting spin $1/2$ fermions