| Summary: | The ground state of the spin-1/2 kagome antiferromagnet remains uncertain despite decades of active research. Here we step aside from this debated question to address the ground-state nature of a related, and potentially just as rich, system made of corner-sharing triangles: the square kagome lattice (SKL). Our work is motivated by the recent synthesis of a distorted SKL compound mentioned by Morita and Tohyama [J. Phys. Soc. Jpn. 87, 043704 (2018)JUPSAU0031-901510.7566/JPSJ.87.043704]. We have studied its spin-1/2 J_{1}-J_{2} phase diagram with an unrestricted Schwinger boson mean-field theory (SBMFT). Our results agree with previous observations of a plaquette phase (J_{2}≪J_{1}) and a ferrimagnet (J_{1}≪J_{2}). In addition, three original phases appear: two incommensurate orders and a topological quantum spin liquid with weak nematicity. The topological order is characterized by fluxes on specific gauge-invariant quantities and the phase is stable under anisotropic perturbations relevant for experiments. Finally, we provide dynamical structure factors of the reported phases that could be observed in inelastic neutron scattering.
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