  We propose a new efficient scheme for the quantum Monte Carlo study of
quantum critical phenomena in quantum spin systems. Rieger and Young's
Trotter-number-dependent finite-size scaling in quantum spin systems and Ito
{\it et al.}'s evaluation of the transition point with the non-equilibrium
relaxation in classical spin systems are combined and generalized. That is,
only one Trotter number and one inverse temperature proportional to system
sizes are taken for each system size, and the transition point of the
transformed classical spin model is estimated as the point at which the order
parameter shows power-law decay. The present scheme is confirmed by the
determination of the critical phenomenon of the one-dimensional $S=1/2$
asymmetric XY model in the ground state. The estimates of the transition point
and the critical exponents $\beta$, $\gamma$ and $\nu$ are in good agreement
with the exact solutions. The dynamical critical exponent is also estimated as
${\mit \Delta}=2.14(I4(Jpm 0.06$, which is consistent with that of the
two-dimensional Ising model.
