Abstract
Recently, a minimal membrane description of the entanglement dynamics of large regions in generic chaotic systems was conjectured in arXiv:1803.00089. Analytic results in random circuits and spin chain numerics support this theory. We show that the results found by the author in arXiv:1612.00082 about the dynamics of entanglement entropy in theories with a holographic dual can be reformulated in terms of the same minimal membrane, providing strong evidence that the membrane theory describes all chaotic systems. We discuss the implications of our results for tensor network approaches to holography and the holographic renormalization group.
Highlights
The dynamics of entanglement entropy in a closed quantum system out of equilibrium is among the most fundamental aspects of thermalization, which has been a subject of recent intense activity in many branches of physics [1,2,3,4,5,6]
Chaotic systems unitarily evolving from a homogenous short-range entangled high energy initial state are expected to “erase the memory” of the fine details of the initial state at the local thermalization timescale tloc, universality may emerge in the scaling limit
The main result of this paper is the rewriting of the holographic results of [1] about the dynamics of entanglement entropy in the scaling limit (1) into the membrane theory form proposed by [22]
Summary
The dynamics of entanglement entropy in a closed quantum system out of equilibrium is among the most fundamental aspects of thermalization, which has been a subject of recent intense activity in many branches of physics [1,2,3,4,5,6]. Based on earlier analytic results in random circuits [21] and spin chain numerics, Jonay, Huse, and Nahum proposed a minimal membrane theory of entropy growth in chaotic systems [22]. In this model, the entropy S1⁄2AðtÞ is given by the energy of a minimal codimension-1 membrane with angle dependent tension EðvÞ, where v stands for the angle with the vertical direction, stretching between two faces of a slab of d-dimensional Minkowski spacetime of height t. By reformulating the holographic entropy computation precisely in terms of the membrane theory, we hope to learn about the relation between tensor network descriptions, entanglement, and the dual gravitational dynamics [23,24,25,26]
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