  Non-equilibrium time evolution in isolated many-body quantum systems
generally results in thermalization. However, the relaxation process can be
very slow, and quasi-stationary non-thermal plateaux are often observed at
intermediate times. The paradigmatic example is a quantum quench in an
integrable model with weak integrability breaking; for a long time, the state
can not escape the constraints imposed by the approximate integrability. We
unveil a new mechanism of prethermalization, based on the presence of a
symmetry of the pre-quench Hamiltonian, which is spontaneously broken at zero
temperature and is explicitly broken by the post-quench Hamiltonian. The
typical time scale of the phenomenon is proportional to the thermal correlation
length of the initial state, which diverges as the temperature is lowered. We
show that the prethermal quasi-stationary state can be approximated by a mixed
state that violates cluster decomposition property. We consider two examples:
the transverse-field Ising chain, where the full time evolution is computed
analytically, and the (non integrable) ANNNI model, which is investigated
numerically.
