Emergent Shastry-Sutherland network from square-kagome Heisenberg antiferromagnet with trimerization

We study the $S=1/2$ square-kagome lattice Heisenberg antiferromagnet with the trimarized modulation. In the trimerized limit, each trimer hosts the four-fold degenearte ground states characterized by the spin and chirality degrees of freedom. We find that, within the first-order perturbation theory with respect to the inter-trimer coupling, the effective Hamiltonian is the Kugel-Khomskii-type model on a Shastry-Sutherland lattice. Based on a mean-field decoupling, we propose a dimer-covering ansatz for the effective Hamiltonian; however, the validity of these states in the low-energy sector remains an open question.