Finite-size prethermalization at the chaos-to-integrable crossover

Abstract

We investigate the infinite temperature dynamics of the complex Sachdev-Ye-Kitaev model (SYK${}_4$) complimented with a single particle hopping term (SYK${}_2$), leading to the chaos-to-integrable crossover of the many-body eigenstates. Due to the presence of the all-to-all connected SYK${}_2$ term, a non-equilibrium prethermal state emerges for a finite time window $t_{th}\propto 2^{a/{\lambda }^{2/5}}$ that scales with the relative interaction strength $\lambda$, between the SYK terms before eventually exhibiting thermalization for all $\lambda$. The scaling of the plateau with $\lambda$ is consistent with the many-body Fock space structure of the time-evolved wave function. In the integrable limit, the wavefunction in the Fock space has a stretched exponential dependence on distance. On the contrary, in the SYK${}_4$ limit, it is distributed equally over the Fock space points characterizing the ergodic phase at long times.

9 pages, 5 figures

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Cited by in corpus (5)

• Thermalization of a Closed Sachdev-Ye-Kitaev System in the Thermodynamic Limit
• Scaling of many-body localization transitions: Quantum dynamics in Fock space and real space
• Prethermalization for Deformed Wigner Matrices
• Universal non-equilibrium dynamics of pure states and density-dependent thermalization in Sachdev-Ye-Kitaev model
• From single-particle to many-body chaos in Yukawa--SYK: theory and a cavity-QED proposal