Entanglement Spreading in a Minimal Model of Maximal Many-Body Quantum Chaos

Bruno Bertini, Pavel Kos, Tomaž Prosen

Research output: Contribution to journalArticlepeer-review

Abstract

The spreading of entanglement in out-of-equilibrium quantum systems is currently at the center of intense interdisciplinary research efforts involving communities with interests ranging from holography to quantum information. Here we provide a constructive and mathematically rigorous method to compute the entanglement dynamics in a class of "maximally chaotic," periodically driven, quantum spin chains. Specifically, we consider the so-called "self-dual" kicked Ising chains initialized in a class of separable states and devise a method to compute exactly the time evolution of the entanglement entropies of finite blocks of spins in the thermodynamic limit. Remarkably, these exact results are obtained despite the maximally chaotic models considered: Their spectral correlations are described by the circular orthogonal ensemble of random matrices on all scales. Our results saturate the so-called "minimal cut" bound and are in agreement with those found in the contexts of random unitary circuits with infinite-dimensional local Hilbert space and conformal field theory. In particular, they agree with the expectations from both the quasiparticle picture, which accounts for the entanglement spreading in integrable models, and the minimal membrane picture, recently proposed to describe the entanglement growth in generic systems. Based on a novel "duality-based" numerical method, we argue that our results describe the entanglement spreading from any product state at the leading order in time when the model is nonintegrable.

Original languageEnglish
Article number021033
JournalPhysical Review X
Volume9
Issue number2
DOIs
Publication statusPublished - 17 May 2019

Bibliographical note

Publisher Copyright:
© 2019 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the »https://creativecommons.org/licenses/by/4.0/» Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

ASJC Scopus subject areas

  • General Physics and Astronomy

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