**Author**
: Alessandro Giuliani

**Title: 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.

**Keywords**:
Hubbard model; ground state energy; upper bound; low density limit.

**Alessandro Giuliani,
Department of Physics,
Princeton University, Princeton 08544 NJ, USA
giuliani@princeton.edu
**