Spin-half Heisenberg antiferromagnet on two archimedian lattices: From the bounce lattice to the maple-leaf lattice and beyond

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 0J^'/JJc^'/J and that the magnetic order parameter varies only weakly with J^'/J. At Jc^'≈1.45J, a transition to a quantum orthogonal-dimer singlet ground state without magnetic long-range order takes place that is probably of first-order type, although we cannot rule out that this transition is second order. 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 find a $1/3$ magnetization plateau for J^'/J1.07 and another one at $2/3$ of saturation emerging only at large J^'/J3.