  We study the effect of site dilution and quantum fluctuations in an
antiferromagnetic spin system on a square lattice within the linear spin-wave
approximation. By performing numerical diagonalization in real space and
finite-size scaling, we characterize the nature of the low-energy spin
excitations for different dilution fractions up to the classical percolation
threshold. We find nontrivial signatures of fractonlike excitations at high
frequencies. Our simulations also confirm the existence of an upper bound for
the amount of quantum fluctuations in the ground state of the system, leading
to the persistence of long-range order up to the percolation threshold. This
result is in agreement with recent neutron-scattering experimental data and
quantum Monte Carlo numerical calculations. We also show that the absence of a
quantum critical point below the classical percolation threshold holds for a
large class of systems whose Hamiltonians can be mapped onto a system of
coupled noninteracting massless bosons.
