  We introduce a variational implementation of cluster perturbation theory
(CPT) to address the dynamics of spin systems driven out of equilibrium. We
benchmark the method with the quantum Ising model subject to a sudden quench of
the transverse magnetic field across the transition or within a phase. We treat
both the one-dimensional case, for which an exact solution is available, as
well the two-dimensional one, for which has to resort to numerical results.
Comparison with exact results shows that the approach provides a quite accurate
description of the real-time dynamics up to a characteristic time scale $\tau$
that increses with the size of the cluster used for CPT. In addition, and not
surprisingly $\tau$ is small for quenches across the equilibrium phase
transition, but can be quite larger for quenches within the ordered or
disordered phases.
