  We study the spin excitation spectra of the two-dimensional spin-$1/2$
Heisenberg model with a checkerboard structures using stochastic analytic
continuation of the imaginary-time correlation function obtained from a quantum
Monte Carlo simulation. The checkerboard models have two different
antiferromagnetic nearest-neighbor interactions $J_{1}$ and $J_{2}$, and the
tuning parameter $g$ is defined as $J_{2}/J_{1}$. The dynamic spin structure
factors are systematically calculated in all phases of the models as well as at
the critical points. To give a full understanding of the dynamic spectra, spin
wave theory is employed to explain some features of numerical results,
especially for the low-energy part. When $g$ is close to $1$, the features of
the spin excitation spectra of each checkerboard model are roughly the same as
those of the original square lattice antiferromagnetic Heisenberg model, and
the high-energy continuum among them is discussed. In contrast to the other
checkerboard structures investigated in this paper, the $3\times 3$
checkerboard model has distinctive excitation features, such as a gap between a
low-energy gapless branch and a gapped high-energy part that exists when $g$ is
small. The gapless branch in this case can be regarded as a spin wave in
N$\mathrm{\acute{e}}$el order formed by a "block spin" in each $3\times 3$
plaquette with an effective exchange interaction originating from
renormalization. One unexpected finding is that the continuum also appears in
this low-energy branch.
