The 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 $J$-$J^{\mathrm{\prime }}$ model interpolating between both systems by varying $J^{\mathrm{\prime }}\mathrm{/}J$ from $J^{\mathrm{\prime }}\mathrm{/}J=0$ (bounce limit) to $J^{\mathrm{\prime }}\mathrm{/}J=1$ (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 ($J^{\mathrm{\prime }}\mathrm{/}J=0$) and maple-leaf ($J^{\mathrm{\prime }}\mathrm{/}J=1$) 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 $J^{\mathrm{\prime }}\mathrm{/}J$. At $J_c^{\mathrm{\prime }}\approx 1.45J$ 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-$J^{\mathrm{\prime }}$ 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 $J’/J \gtrsim 1.07$andanotheroneat2\mathrm{/}3ofsaturationemergingonlyatlarge$J’/J \gtrsim 3$.