Momentum distribution of the one-dimensional hard-core boson Hubbard model

We investigate the momentum distributions, $n_k$, of the one- dimensional hard-core boson Hubbard model as a function of the nearest-neighbor interaction strength by exact diagonalizations for lattices up to 30 sites. It is well known that the ground state of this model shows a quantum phase transition between the Ising-ordered insulating phase and the XY-ordered superfluid phase at $V=2t$. Predetermination of the critical point helps us to investigate various critical behaviors. At the critical point, the momentum distribution shows a linear dependence ($n_k \sim |k-\pi|$). $n_k (k=\pi)$ shows different critical behaviors upon appoaching the critical point in the Ising or XY regions. Some other properties of the momentum distributions and the crtical behaviors are discussed.