Space and Time Renormalization in Phase Transition Dynamics

When a system is driven across a quantum critical point at a constant rate its evolution must become non-adiabatic as the relaxation time τ 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 ξ̂ set at the time t̂=τ̂ 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.