  We present a family of two-dimensional frustrated quantum magnets solely
based on pure nearest-neighbor Heisenberg interactions which can be solved
quasi-exactly. All lattices are constructed in terms of frustrated quantum
cages containing a chiral degree of freedom protected by frustration. The
ground states of these models are dubbed ultimate quantum paramagnets and
exhibit an extensive entropy at zero temperature. We discuss the unusual and
extensively degenerate excitations in such phases. Implications for
thermodynamic properties as well as for decoherence free quantum computation
are discussed.
