  We report on recent results for strongly frustrated quantum $J_1$-$J_2$
antiferromagnets in dimensionality d=1,2,3 obtained by the coupled cluster
method (CCM). We demonstrate that the CCM in high orders of approximation
allows us to investigate quantum phase transitions driven by frustration and to
discuss novel quantum ground states. In detail we consider the ground-state
properties of (i) the Heisenberg spin-1/2 antiferromagnet on the cubic lattice
in d=1,2,3, and use the results for the energy, the sublattice magnetization
and the spin stiffness as a benchmark test for the precision of the method;
(ii) coupled frustrated spin chains (the quasi-one-dimensional $J_1$--$J_2$
model) and discuss the influence of the quantum fluctuations and the interchain
coupling on the incommensurate spiral state present in the classical model;
(iii) the Shastry-Sutherland antiferromagnet on the square lattice; and (iv) a
stacked frustrated square-lattice Heisenberg antiferromagnet (the
quasi-two-dimensional $J_1$--$J_2$ model), and discuss the influence of the
interlayer coupling on the quantum paramagnetic ground-state phase that is
present for the strictly two-dimensional model.
