Black holes often saturate entanglement entropy the fastest

• URL: http://arxiv.org/abs/2001.03172v3
• Date: Wed, 9 Dec 2020 15:40:57 GMT
• Title: Black holes often saturate entanglement entropy the fastest
• Authors: M\'ark Mezei and Wilke van der Schee
• Abstract summary: We show that in systems with a holographic dual, the saturation time is equal to this lower bound for a variety of differently shaped entangling surfaces. This finding adds to the growing list of tasks that black holes are the fastest at.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: There is a simple bound on how fast the entanglement entropy of a subregion of a many-body quantum system can saturate in a quench: $t_\text{sat}\geq R/v_B$, where $t_\text{sat}$ is the saturation time, $R$ the radius of the largest inscribed sphere, and $v_B$ the butterfly velocity characterizing operator growth. By combining analytic and numerical approaches, we show that in systems with a holographic dual, the saturation time is equal to this lower bound for a variety of differently shaped entangling surfaces, implying that the dual black holes saturate the entanglement entropy as fast as possible. This finding adds to the growing list of tasks that black holes are the fastest at. We furthermore analyze the complete time evolution of entanglement entropy for large regions with a variety of shapes, yielding more detailed information about the process of thermalization in these systems.

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