  Fermions and hardcore bosons share the same restriction: no more than one
particle can occupy a single site in a lattice system. Specifically, in one
dimension, two systems can share the same matrix representation. In this work,
we investigate both the fermion and hardcore-boson models with nearest-neighbor
(NN) interaction in a ring lattice. We construct the exact eigenstates of the
hardcore-boson model with resonant NN interaction and show that they possess
off-diagonal long-range order (ODLRO) in the thermodynamic limit. In
comparison, the fermionic counterpart does not support such a feature due to
the different particle statistics, although they share an identical energy
spectrum. In addition, we examine the effect of the periodic boundary condition
on the dynamics of the condensate states through numerical simulations.
