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We investigate ground states of $s$=1/2 Heisenberg antiferromagnets on theeleven two-dimensional (2D) Archimedian lattices by using the coupled clustermethod. Magnetic interactions and quantum fluctuations play against each othersubtly in 2D quantum magnets and the magnetic ordering is thus sensitive to thefeatures of lattice topology. Archimedean lattices are those lattices that have2D arrangements of regular polygons and they often build the underlyingmagnetic lattices of insulating quasi-two-dimensional quantum magneticmaterials. Hence they allow a systematic study of the relationship betweenlattice topology and magnetic ordering. We find that the Archimedian latticesfall into three groups: those with semiclassical magnetic ground-statelong-range order, those with a magnetically disordered (cooperative quantumparamagnetic) ground state, and those with a fragile magnetic order. The mostrelevant parameters affecting the magnetic ordering are the coordination numberand the degree of frustration present.

Quantum s = 1/2 Antiferromagnets on Archimedean Lattices: The Route from Semiclassical Magnetic Order to Nonmagnetic Quantum States