Thermalization of randomly coupled SYK models
Thermalization of randomly coupled SYK models
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DOI：
10.1088/1742-5468/ac416b
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发表时间：
2021-09
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影响因子：
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通讯作者：
R. Sohal;L. Nie;Xiao-Qi Sun;E. Fradkin
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作者：
R. Sohal;L. Nie;Xiao-Qi Sun;E. Fradkin
从纠缠的角度研究了猝灭后通过随机相互作用耦合的Sachdev-Ye-Kitaev（SYK）模型的热化。以前的研究表明，当两个SYK模型通过随机二体项耦合的系统从具有足够低的有效温度的热场双态淬灭时，Rényi熵不会饱和到大N极限下的预期热值。使用数值大N方法，我们首先表明，Rényi熵在一对SYK模型耦合的两体项可以热化，如果淬火从一个状态具有足够高的有效温度，因此表现出状态相关的热化。相比之下，由单体项耦合的SYK模型似乎总是热化。我们提供的证据表明，在前一个系统的亚热行为可能是一个大N的假象，通过重复淬火有限N和发现的饱和值的雷尼熵外推到期望的热值在N → ∞极限。最后，作为一个更细粒度的热化措施，我们计算淬火后的约化密度矩阵的后期频谱形状因子。虽然一个单一的SYK点表现出完美的协议与随机矩阵理论，无论是二次和四次耦合SYK模型表现出轻微的偏差。
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.