Thermalization of Randomly Coupled SYK Models
arXiv:2110.00017 · doi:10.1088/1742-5468/ac416b
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- limit. Using numerical large- 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- artifact by repeating the quench for finite and finding that the saturation value of the Rényi entropy extrapolates to the expected thermal value in the 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.
arXiv commentv1: 41 pages single column, 14 figures; v2: Additional references; v3: Minor revisions
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