Ground state energy of the low density Hubbard model

Robert Seiringer Department of Physics, Jadwin Hall, Princeton University Jun Yin Department of Physics, Jadwin Hall, Princeton University

Mathematical Physics mathscidoc:1608.22016

Journal of Statistical Physics, 131, (6), 1139-1154, 2008
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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@inproceedings{robert2008ground,
  title={Ground state energy of the low density Hubbard model},
  author={Robert Seiringer, and Jun Yin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160824110558012793433},
  booktitle={Journal of Statistical Physics},
  volume={131},
  number={6},
  pages={1139-1154},
  year={2008},
}
Robert Seiringer, and Jun Yin. Ground state energy of the low density Hubbard model. 2008. Vol. 131. In Journal of Statistical Physics. pp.1139-1154. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160824110558012793433.
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