Periodically Driven Sachdev-Ye-Kitaev Models

Periodically driven quantum matter can realize exotic dynamical phases. In order to understand how ubiquitous and robust these phases are, it is pertinent to investigate the heating dynamics of generic interacting quantum systems. Here we study the thermalization in a periodically driven generalized Sachdev-Ye-Kitaev (SYK) model, which realizes a crossover from a heavy Fermi liquid (FL) to a non-Fermi liquid (NFL) at a tunable energy scale. Developing an exact field theoretic approach, we determine two distinct regimes in the heating dynamics. While the NFL heats exponentially and thermalizes rapidly, we report that the presence of quasiparticles in the heavy FL obstructs heating and thermalization over comparatively long timescales. Prethermal high-frequency dynamics and possible experimental realizations of nonequilibrium SYK physics are discussed as well.

Figure 1

A periodically driven Sachdev-Ye-Kitaev model. Illustration of a generalized SYK model with periodically modulated hopping terms (red ellipses) and a static interaction Hamiltonian (blue ellipses). The drive of the hopping is illustrated by the red wiggly lines.

Figure 2

Energy absorption. (a) Driving the strange metal leads to a rapid exponential heating as confirmed for a variety of drive parameters. (b) The driven heavy Fermi liquid displays a crossover from slow to exponential heating when $\mathrm{\Omega }\lesssim K^2/J$. By contrast, for $\mathrm{\Omega }\gtrsim K^2/J$ the dynamics becomes exponential rather quickly.

Figure 3

Fluctuation-dissipation relations under periodic driving. (a) For the driven strange metal, the effective temperature $T_{\mathrm{eff}}(t)$ obtained from FDRs quickly agrees with the instantaneous temperature $T_{\mathrm{inst}}(t)$ obtained from assuming thermal equilibrium at the instantaneous energy density, see Eq. (5), highlighting the fast thermalization. (b) FDRs at four different stroboscopic times indicated by the arrows in (a). (c) The Fermi liquid fails to thermalize for long times, indicated by the deviations between the two temperatures. (d) The corresponding FDRs are steplike and are only fulfilled at low energies.

Figure 4

Fast driving. (a) The exact energy density of the system (blue) shows good agreement with the evolution of an effective Floquet Hamiltonian (green dash-dotted line). Turning on the rapid drive acts as a quantum quench, after which the system effectively stops absorbing energy and enters a prethermal plateau. (b) In this prethermal regime the system is thermal, see FDRs in the inset, with a temperature that is nearly constant but slowly increasing. Only after long times the system can heat up to infinite temperature.