| We consider the spin-1/2 antiferromagnetic Heisenberg model on three frustrated lattices (diamond and dimer-plaquette chains and 2D square-kagome lattice) with almost dispersionless lowest magnon band. Eliminating high-energy degrees of freedom at high magnetic field, we construct low-energy effective Hamiltonians which are much simpler than the initial ones. This allows a more extended analytical and numerical analysis. In addition to the standard strong-coupling perturbation theory we also use an localized-magnon based approach leading to a substantial improvement of the strong-coupling approach. We perform extensive exact diagonalization studies to check the quality of different effective Hamiltonian. Finally, based on the effective-model description we examine the properties of the considered frustrated quantum Heisenberg antiferromagnets at high fields and low temperatures. We also apply our approach to explore the high-field thermodynamic properties for a generalized diamond spin chain model for azurite. |
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