title: Ground-state energies of spinless free fermions and hard-core bosons.
abstract: 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 have a higher ground-state energy than fermions. We prove rigorously that this inversion indeed occurs in several examples.
authors.affiliation: Institute for Solid State Physics, University of Tokyo, Kashiwa 277-8581, Japan.
authors.forename: Wenxing
authors.initials: W
authors.lastname: Nie
authors.affiliation: Department of Physics, Gakushuin University, Tokyo 171-8588, Japan.
authors.forename: Hosho
authors.initials: H
authors.lastname: Katsura
authors.affiliation: Institute for Solid State Physics, University of Tokyo, Kashiwa 277-8581, Japan.
authors.forename: Masaki
authors.initials: M
authors.lastname: Oshikawa