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We consider the spin-1/2 antiferromagnetic Heisenberg model on thetwo-dimensional square-kagome lattice with almost dispersionless lowest magnonband. For a general exchange coupling geometry we elaborate low-energyeffective Hamiltonians which emerge at high magnetic fields. The effectivemodel to describe the low-energy degrees of freedom of the initial frustratedquantum spin model is the (unfrustrated) square-lattice spin-1/2 $XXZ$ model ina $z$-aligned magnetic field. For the effective model we perform quantum MonteCarlo simulations to discuss the low-temperature properties of thesquare-kagome quantum Heisenberg antiferromagnet at high magnetic fields. Wepay special attention to a magnetic-field drivenBerezinskii-Kosterlitz-Thouless phase transition which occurs at lowtemperatures.

The square-kagome quantum Heisenberg antiferromagnet at high magnetic fields: The localized-magnon paradigm and beyond