2021/10/31 by Ramanjit Sohal, Laimei Nie, Xiao-Qi Sun +1 · 1 citation
Physics and Astronomy · #cond-mat.str-el #cond-mat.stat-mech #hep-th
paper · pdf · doi:10.1088/1742-5468/ac416b
published as J. Stat. Mech. (2022) 013103 · v1: 41 pages single column, 14 figures; v2: Additional references; v3: Minor revisions
arxiv created 2021/12/16 · arxiv updated 2022/01/25
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.