  The site- and bond-dilution effects of the nonmagnetic ground state of a
two-dimensional $S=1/2$ antiferromagnetic Heisenberg model, coupled with the
lattice distortions on a square lattice, are investigated by performing quantum
Monte Carlo simulations. In the nondiluted system, a phase diagram
parameterized by the interchain interaction and the elastic constant is
obtained, and the values of the lattice distortions in the dimerized phase are
evaluated precisely. In the diluted system, we compare two ground-state
energies assuming two patterns of lattice distortions with magnetic moments
(effective spins) induced near the diluted parts and induced at the midpoint
between the diluted parts. As a result, we find that it is difficult to induce
effective spins near diluted parts for large elastic constants, small
interchain interactions, and large concentrations of dilution.
