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We investigate the ground state of the two-dimensional Heisenbergantiferromagnet on two Archimedean lattices, namely, the maple-leaf and bouncelattices as well as a generalized $J$-$J'$ model interpolating between bothsystems by varying $J'/J$ from $J'/J=0$ (bounce limit) to $J'/J=1$ (maple-leaflimit) and beyond. We use the coupled cluster method to high orders ofapproximation and also exact diagonalization of finite-sized lattices todiscuss the ground-state magnetic long-range order based on data for theground-state energy, the magnetic order parameter, the spin-spin correlationfunctions as well as the pitch angle between neighboring spins. Our resultsindicate that the "pure" bounce ($J'/J=0$) and maple-leaf ($J'/J=1$) Heisenbergantiferromagnets are magnetically ordered, however, with a sublatticemagnetization drastically reduced by frustration and quantum fluctuations. Wefound 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 onlyweakly with $J'/J$. At $J'_c \approx 1.45 J$ a direct first-order transition toa quantum orthogonal-dimer singlet ground state without magnetic long-rangeorder takes place. The orthogonal-dimer state is the exact ground state in thislarge-$J'$ regime, and so our model has similarities to the Shastry-Sutherlandmodel. Finally, we use the exact diagonalization to investigate themagnetization curve. We a find a 1/3 magnetization plateau for $J'/J \gtrsim1.07$ and another one at 2/3 of saturation emerging only at large $J'/J \gtrsim3$.

The spin-half Heisenberg antiferromagnet on two Archimedian lattices: From the bounce lattice to the maple-leaf lattice and beyond