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

We investigate the infinite-temperature dynamics of complex Sachdev-Ye-Kitaev model $({\mathrm{SYK}}_{4})$ complemented with a single-particle hopping term $({\mathrm{SYK}}_{2})$, leading to chaos-to-integrable crossover many-body eigenstates. Due presence all-to-all connected ${\mathrm{SYK}}_{2}$ term, nonequilibrium prethermal state emerges for finite time window ${t}_{\mathrm{th}}\ensuremath{\propto}{2}^{a/{\ensuremath{\lambda}}^{2/5}}$ that scales relative interaction strength $\ensuremath{\lambda}$, between SYK terms before eventually exhibiting thermalization all $\ensuremath{\lambda}$. The scaling plateau $\ensuremath{\lambda}$ is consistent Fock-space structure time-evolved wave function. In integrable limit, function in Fock space has stretched exponential dependence on distance. On contrary, ${\mathrm{SYK}}_{4}$ it distributed equally over points characterizing ergodic phase at long times.