  We consider the spin-1/2 antiferromagnetic Heisenberg model on the
two-dimensional square-kagome lattice with almost dispersionless lowest magnon
band. For a general exchange coupling geometry we elaborate low-energy
effective Hamiltonians which emerge at high magnetic fields. The effective
model to describe the low-energy degrees of freedom of the initial frustrated
quantum spin model is the (unfrustrated) square-lattice spin-1/2 $XXZ$ model in
a $z$-aligned magnetic field. For the effective model we perform quantum Monte
Carlo simulations to discuss the low-temperature properties of the
square-kagome quantum Heisenberg antiferromagnet at high magnetic fields. We
pay special attention to a magnetic-field driven
Berezinskii-Kosterlitz-Thouless phase transition which occurs at low
temperatures.
