Nonequilibrium variational cluster perturbation theory: Quench dynamics of the quantum Ising model

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 case, for which we have 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 timescale τ that increases with the size of the cluster used for CPT. In addition, and not surprisingly, τ is small for quenches across the equilibrium phase transition point, but can be quite larger for quenches within the ordered or disordered phases.