Entanglement spreading in a minimal model of maximal many-body quantum chaos

Bertini, Bruno (author), Kos, Pavel (author), Prosen, Tomaž (author)

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.

• Language: English
• Keywords: quantum statistical mechanics, nonequilibrium systems, many-body systems, quantum entanglement
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2019
• Number of pages: Str. 021033-1-021033-27
• Numbering: Vol. 8, iss. 2
• PID: 20.500.12556/RUL-107760
• UDC: 530.145
• ISSN on article: 2160-3308
• DOI: 10.1103/PhysRevX.9.021033
• COBISS.SI-ID: 3312740
• Publication date in RUL: 23.05.2019

Record is a part of a journal

• Title: Physical review
• Shortened title: Phys. rev., X
• Publisher: American Physical Society
• ISSN: 2160-3308
• COBISS.SI-ID: 19686152

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.
• Licensing start date: 23.05.2019

Secondary language

• Language: Slovenian
• Keywords: kvantna statistična mehanika, neravnovesni sistemi, večdelčni sistemi, kvantna prepletenost

Projects

• Funder: EC - European Commission
• Funding programme: H2020
• Project number: 694544
• Name: Open many-body non-equilibrium systems
• Acronym: OMNES