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

## TL;DR

This paper investigates the thermalization dynamics of a model transitioning from a non-Fermi liquid to a Fermi liquid, revealing rapid thermalization after quenches to NFL and complex slow-quench behavior influenced by residual entropy.

## Contribution

It introduces a model coupling SYK fermions to lead fermions, analyzing thermalization and residual entropy effects across the NFL-FL transition with novel non-analytic scaling results.

## Key findings

- Rapid thermalization after sudden quench to NFL.
- Multiple prethermal regimes after quench to FL.
- Intermediate-$\tau$ non-analytic power-law energy scaling.

## Abstract

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 $\tau$, we find that the excitation energy generated has a remarkable intermediate-$\tau$ non-analytic power-law dependence, $\tau^{-\eta}$ with $\eta<1$, 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 $\tau\to\infty$, signaling a violation of adiabaticity, due to the residual entropy present in the SYK fermions.