  We investigate the ground state of the two-dimensional Heisenberg
antiferromagnet on two Archimedean lattices, namely, the maple-leaf and bounce
lattices as well as a generalized $J$-$J'$ model interpolating between both
systems by varying $J'/J$ from $J'/J=0$ (bounce limit) to $J'/J=1$ (maple-leaf
limit) and beyond. We use the coupled cluster method to high orders of
approximation and also exact diagonalization of finite-sized lattices to
discuss the ground-state magnetic long-range order based on data for the
ground-state energy, the magnetic order parameter, the spin-spin correlation
functions as well as the pitch angle between neighboring spins. Our results
indicate that the "pure" bounce ($J'/J=0$) and maple-leaf ($J'/J=1$) Heisenberg
antiferromagnets are magnetically ordered, however, with a sublattice
magnetization drastically reduced by frustration and quantum fluctuations. We
found that magnetic long-range order is present in a wide parameter range $0
\le J'/J \lesssim J'_c/J $ and that the magnetic order parameter varies only
weakly with $J'/J$. At $J'_c \approx 1.45 J$ a direct first-order transition to
a quantum orthogonal-dimer singlet ground state without magnetic long-range
order takes place. The orthogonal-dimer state is the exact ground state in this
large-$J'$ regime, and so our model has similarities to the Shastry-Sutherland
model. Finally, we use the exact diagonalization to investigate the
magnetization curve. We a find a 1/3 magnetization plateau for $J'/J \gtrsim
1.07$ and another one at 2/3 of saturation emerging only at large $J'/J \gtrsim
3$.
