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Abstract We investigate the thermalization of Sachdev–Ye–Kitaev (SYK) models coupled via random interactions following quenches from the perspective of entanglement. Previous studies have shown that when a system of two SYK models coupled by random two-body terms is quenched from the thermofield double state with sufficiently low effective temperature, the Rényi entropies do not saturate to the expected thermal values in the large- N limit. Using numerical large- N methods, we first show that the Rényi entropies in a pair SYK models coupled by two-body terms can thermalize, if quenched from a state with sufficiently high effective temperature, and hence exhibit state-dependent thermalization. In contrast, SYK models coupled by single-body terms appear to always thermalize. We provide evidence that the subthermal behavior in the former system is likely a large- N artifact by repeating the quench for finite N and finding that the saturation value of the Rényi entropy extrapolates to the expected thermal value in the N → ∞ limit. Finally, as a finer grained measure of thermalization, we compute the late-time spectral form factor of the reduced density matrix after the quench. While a single SYK dot exhibits perfect agreement with random matrix theory, both the quadratically and quartically coupled SYK models exhibit slight deviations. 

In the development of topological photonics, achieving three-dimensional topological insulators is of notable interest since it enables the exploration of new topological physics with photons and promises novel photonic devices that are robust against disorders in three dimensions. Previous theoretical proposals toward three-dimensional topological insulators use complex geometries that are challenging to implement. On the basis of the concept of synthetic dimension, we show that a two-dimensional array of ring resonators, which was previously demonstrated to exhibit a two-dimensional topological insulator phase, automatically becomes a three-dimensional topological insulator when the frequency dimension is taken into account. Moreover, by modulating a few of the resonators, a screw dislocation along the frequency axis can be created, which provides robust one-way transport of photons along the frequency axis. Demonstrating the physics of screw dislocation in a topological system has been a substantial challenge in solid-state systems. Our work indicates that the physics of three-dimensional topological insulators can be explored in standard integrated photonic platforms, leading to opportunities for novel devices that control the frequency of light.