  We study the connections among particle statistics, frustration, and
ground-state energy in quantum many-particle systems. In the absence of
interaction, the influence of particle statistics on the ground-state energy is
trivial: the ground-state energy of noninteracting bosons is lower than that of
free fermions because of Bose-Einstein condensation and Pauli exclusion
principle. In the presence of hard-core or other interaction, however, the
comparison is not trivial. Nevertheless, the ground-state energy of hard-core
bosons is proved to be lower than that of spinless fermions, if all the hopping
amplitudes are nonnegative. The condition can be understood as the absence of
frustration among hoppings. By mapping the many-body Hamiltonian to a
tight-binding model on a fictitious lattice, we show that the Fermi statistics
of the original particles introduces an effective magnetic flux in the
fictitious lattice. The latter can be regarded as a frustration, since it leads
to a destructive interference among different paths along which a single
particle is propagating. If we introduce hopping frustration, the hopping
frustration is expected to compete with "effective frustration", leading to the
possibility that the ground-state energy of hard-core bosons can be higher than
that of fermions. We present several examples, in which the ground-state energy
of hard-core bosons is proved to be higher than that of fermions due to the
hopping frustration. The basic ideas were reported in a recent Letter [W.-X.
Nie, H. Katsura, and M. Oshikawa, Phys. Rev. Lett. 111, 100402 (2013)]; more
details and several extensions, including one to the spinful case, are
discussed in the present paper.
