Ground state energy of the low density Hubbard model

Details Ground state energy of the low density Hubbard model Ground state energy of the low density Hubbard model

2007-12-17

arxiv.org/abs/0712.2810v1

J. Stat. Phys. 131, 1139 (2008)

Physics

Mathematical Physics

LaTeX2e, 18 pages

Scientific paper

10.1007/s10955-008-9527-x

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, 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 $8\pi a \rho_u \rho_d$, where $\rho_{u(d)}$ 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.

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