  We have computed the low energy quantum states and low frequency dynamical
susceptibility of complex quantum spin systems in the limit of strong
interactions, obtaining exact results for system sizes enormously larger than
accessible previously. The ground state is a complex superposition of a
substantial fraction of all the classical ground states, and yet the dynamical
susceptibility exhibits sharp resonances reminiscent of the behavior of single
spins. These results show that strongly interacting quantum systems can
organize to generate coherent excitations and shed light on recent experiments
demonstrating that coherent excitations are present in a disordered spin
liquid. The dependence of the energy spectra on system size differs
qualitatively from that of the energy spectra of random undirected bipartite
graphs with similar statistics, implying that strong interactions are giving
rise to these unusual spectral properties.
