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

TL;DR

This paper establishes an upper bound on the ground state energy of the 3D Hubbard model at low densities, confirming the conjecture that the ground state spin vanishes as density approaches zero.

Contribution

It provides the first rigorous derivation of the low-density asymptotic ground state energy for the 3D Hubbard model, matching continuum Fermi gas results.

Findings

Upper bound matches the dilute Fermi gas asymptotics

Confirms the vanishing total spin conjecture at low densities

Bridges lattice Hubbard model with continuum Fermi gas results

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.