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Ground State Energy of the Low Density Hubbard Model
Authors:Robert Seiringer  Jun Yin
Institution:(1) Department of Physics, Jadwin Hall, Princeton University, Princeton, NJ 08542-0708, USA
Abstract:We derive a lower bound on the ground state energy of the Hubbard model for given value of the total spin. In combination with the upper bound derived previously by Giuliani (J. Math. Phys. 48:023302, 2007]), our result proves that in the low density limit the leading order correction compared to the ground state energy of a non-interacting lattice Fermi gas is given by 8π a ? u ? d , where ? u(d) denotes the density of the spin-up (down) particles, and a is the scattering length of the contact interaction potential. This result extends previous work on the corresponding continuum model to the lattice case.
Keywords:Hubbard model  Scattering length  Ground state energy  Thermodynamic limit
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