The task of exploring and understanding important aspects of
far-from-equilibrium dynamics of closed and generic quantum many-body systems
has received a thrust of attention in recent years, driven partly by remarkable
advances in ultracold experimental technologies. In this work, for the
paradigmatic Ising spin chain with transverse and longitudinal fields, we
present numerical observations of several “fine-grained” features of
far-from-equilibrium dynamics from a quantum informational point of view that
have hitherto escaped notice, induced by quantum quenches across the Ising
critical point between states deep inside the para- and ferromagnetic regimes.
Rather featureless dynamics is seen for ferromagnetic to paramagnetic quenches,
but paramagnetic to ferromagnetic quenches exhibit rich behaviour, including a
series of sudden deaths and revivals of entanglement between two spins in the
system’s bulk, periodic but short-lived occurrences of approximately
$1-$uniform states and recurrences of an approximately Page-like dynamics of
entanglement entropies of one- and two-spin subsystems, non-analytic cusps in
single-copy entanglement entropy for sufficiently big subsystems, insufficient
mixedness and a series of scrambling-$\textit{un}$scrambling of local
information between neighboring spins. Moreover, essentially indistinguishable
dynamics is seen at very early times between the integrable limit (zero
longitudinal field) and non-integrable cases, with the former eventually
showing signatures of better mixing and faster approach to equilibration than
the latter. These features are expected to hold for quench dynamics across
Ising quantum critical points in more complicated systems.

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