Thermalization of non-Fermi-liquid electron-phonon systems: Hydrodynamic relaxation of the Yukawa-Sachdev-Ye-Kitaev model

TL;DR

This paper investigates how a non-Fermi-liquid electron-phonon system thermalizes, revealing faster fermion thermalization, a hydrodynamic relaxation process, and universal relaxation rates dependent on the system's low energy spectrum.

Contribution

It introduces a hydrodynamic approximation to describe thermalization in a Yukawa-Sachdev-Ye-Kitaev model coupled to a thermal bath, highlighting universal relaxation behavior.

Findings

Fermions thermalize faster than phonons in the non-Fermi-liquid regime.

System exhibits a quasi-thermal distribution characterized by a time-dependent effective temperature.

Relaxation rates depend universally on the low energy spectrum and final temperature.

Abstract

We study thermalization dynamics in a fermion-phonon variant of the Sachdev-Ye-Kitaev model coupled to an external cold thermal bath of harmonic oscillators. We find that quantum critical fermions thermalize more efficiently than phonons, in sharp contrast to the behavior in the Fermi liquid regime. In addition, after a short prethermal stage, the system acquires a quasi-thermal distribution given by a time-dependent effective temperature, reminiscent of "hydrodynamic" relaxation. All physical observables relax at the same rate which scales with the final temperature through an exponent that depends universally on the low energy spectrum of the system and the bath. Such relaxation rate is derived using a hydrodynamic approximation in full agreement with the numerical solution of a set quantum kinetic equations derived from the Keldysh formalism for non-equilibrium Green's functions. Our results hint toward further research on the applicability of the hydrodynamic picture in the description of the late time dynamics of open quantum systems despite the absence of conserved quantities in regimes dominated by conserving collisions.