Out-of-equilibrium dynamics and thermalization across a solvable non-Fermi liquid to Fermi liquid transition*

We study the non-equilibrium dynamics of an interacting model [1] 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 on N sites quadratically coupled to non-interacting peripheral fermions on M sites. The transition from the NFL (p < 1) to FL (p > 1) is obtained at p=1 by tuning the ratio p=M/N. We study the dynamics as a function of p, (a) after a quench where the coupling between initially disconnected SYK and peripheral fermions is suddenly switched on, and (b) during a slow quench when the coupling is slowly ramped over a duration τ. In the sudden quench, we find that a thermal state is reached in the NFL (p < 1) through collapse-revival oscillations of the quasiparticle residue of the peripheral fermions. In the FL phase, the system fails to thermalize within the accessible time and shows multiple pre-thermal regimes. In the slow quench, the excitation energy generated has a power-law dependence ∼τ ^−η for intermediate τ, with a strong p-dependent η having a minimum at the transition. At larger τ the power-law breaks down, along with adiabaticity, due to the initial residual entropy of the SYK fermions. [1] S. Banerjee and E. Altman, PRB 95, 134302 (2017).