  We introduce, and determine decoherence for, a wide class of non-trivial
quantum spin baths which embrace Ising, XY and Heisenberg universality classes
coupled to a two-level system. For the XY and Ising universality classes we
provide an exact expression for the decay of the loss of coherence beyond the
case of a central spin coupled uniformly to all the spins of the baths which
has been discussed so far in the literature. In the case of the Heisenberg spin
bath we study the decoherence by means of the time-dependent density matrix
renormalization group. We show how these baths can be engineered, by using
atoms in optical lattices.
