  When a system is driven across a quantum critical point at a constant rate
its evolution must become non-adiabatic as the relaxation time $\tau$ diverges
at the critical point. According to the Kibble-Zurek mechanism (KZM), the
emerging post-transition excited state is characterized by a finite correlation
length $\hat\xi$ set at the time $\hat t=\hat \tau$ when the critical slowing
down makes it impossible for the system to relax to the equilibrium defined by
changing parameters. This observation naturally suggests a dynamical scaling
similar to renormalization familiar from the equilibrium critical phenomena. We
provide evidence for such KZM-inspired spatiotemporal scaling by investigating
an exact solution of the transverse field quantum Ising chain in the
thermodynamic limit.
