Ground-state energies of spinless free fermions and hard-core bosons.

@article{Nie2013GroundstateEO,
  title={Ground-state energies of spinless free fermions and hard-core bosons.},
  author={Wenxing Nie and Hosho Katsura and Masaki Oshikawa},
  journal={Physical review letters},
  year={2013},
  volume={111 10},
  pages={
          100402
        }
}
We compare the ground-state energies of bosons and fermions with the same form of the Hamiltonian. If both are noninteracting, the ground-state energy of bosons is always lower, owing to Bose-Einstein condensation. However, the comparison is nontrivial when bosons do interact. We first prove that, when the hopping is unfrustrated (all the hopping amplitudes are non-negative), hard-core bosons still must have a lower ground-state energy than fermions. If the hopping is frustrated, bosons can… 

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