Prethermalization and dynamical transition in an isolated trapped ion spin chain

We propose an experimental scheme to observe prethermalization and dynamical
transition in one-dimensional XY spin chain with long range interaction and
inhomogeneous lattice spacing, which can be readily implemented with the
recently developed trapped-ion quantum simulator. Local physical observables
are found to relax to prethermal values at intermediate time scale, followed by
complete relaxation to thermal values at much longer time. The physical origin
of prethermalization is explained by spotting a non-trivial structure in lower
half of the energy spectrum. The dynamical behavior of the system is shown to
cross difference phases when the interaction range is continuously tuned,
indicating the existence of dynamical phase transition.