  We consider a class of global quantum quenches in the Heisenberg XXZ spin
chain, where the initial states are given by products of local two-site states.
The two main examples are the N\'eel state and the dimer state. We derive an
exact analytic result for the "Loschmidt echo per site" at imaginary times and
also consider the analytic continuation back to real times. As a by-product we
obtain an exact result for the "overlap per site" between the N\'eel state and
the ground state of the XXZ Hamiltonian in the massive regime.
