Dimensional reduction in quantum spin- 12 system on a 17 -depleted triangular lattice

We study the magnetism of a quantum spin-$\frac{1}{2}$ antiferromagnet on a maple-leaf lattice which is obtained by regularly depleting $\frac{1}{7}$ of the sites of a triangular lattice. Although the interactions are set to be spatially isotropic, the ground state shows a stripe N\'eel order and the temperature dependence of magnetic susceptibility follows that of the one-dimensional XXZ model with a finite spin gap. We examine the nature of frustration by mapping the low-energy degenerate manifold of states to the fully packed loop-string model on a dual cluster-depleted honeycomb lattice, finding that the order-by-disorder due to quantum fluctuation characteristic of highly frustrated magnets is responsible for the emergent stripes. The excited magnons split into two spinons and propagate in the one-dimensional direction along the stripe, which is reminiscent of the XXZ or Ising model in one dimension. Unlike most of the previously studied dimensional-reduction effects, our case is purely spontaneous as the interactions of the Hamiltonian retain a two-dimensional structure.