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Quench, thermalization and residual entropy across a non-Fermi liquid to Fermi liquid transition

We study the thermalization, after sudden and slow quenches, of an interacting model having a quantum phase transition from a Sachdev-Ye-Kitaev (SYK) non-Fermi liquid (NFL) to a Fermi liquid (FL). The model has SYK fermions coupled to non-interacting lead fermions and can be realized in a graphene flake connected to external leads. After a sudden quench to the NFL, a thermal state is reached rapidly via collapse-revival oscillations of the quasiparticle residue of the lead fermions. In contrast, the quench to the FL, across the NFL-FL transition, leads to multiple prethermal regimes and much slower thermalization. In the slow quench performed over a time $τ$, we find that the excitation energy generated has a remarkable intermediate-$τ$ non-analytic power-law dependence, $τ^{-η}$ with $η<1$, which seemingly masks the dynamical manifestation of the initial residual entropy of the SYK fermions. The power-law scaling is expected to eventually break down for $τ\to\infty$, signaling a violation of adiabaticity, due to the residual entropy present in the SYK fermions.