Application of Symmetry Methods to Low-Dimensional Heisenberg Magnets

An account of symmetry is very fruitful in studies of quantum spin systems. In the present paper we demonstrate how to use the spin SU(2) and the point symmetries in optimization of the theoretical condensed matter tools: the exact diagonalization, the renormalization group approach, the cluster perturbation theory. We apply the methods for study of Bose-Einstein condensation in dimerized antiferromagnets, for investigations of magnetization processes and magnetocaloric effect in quantum ferrimagnetic chain.