Entanglement Spreading in a Minimal Model of Maximal Many-Body Quantum Chaos
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 compu...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2019-05-01
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| Series: | Physical Review X |
| Online Access: | http://doi.org/10.1103/PhysRevX.9.021033 |
| _version_ | 1798033232233496576 |
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| author | Bruno Bertini Pavel Kos Tomaž Prosen |
| author_facet | Bruno Bertini Pavel Kos Tomaž Prosen |
| author_sort | Bruno Bertini |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T20:27:00Z |
| format | Article |
| id | doaj.art-4cfa00a828ce41af9367ec5b931847c3 |
| institution | Directory Open Access Journal |
| issn | 2160-3308 |
| language | English |
| last_indexed | 2024-04-11T20:27:00Z |
| publishDate | 2019-05-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review X |
| spelling | doaj.art-4cfa00a828ce41af9367ec5b931847c32022-12-22T04:04:38ZengAmerican Physical SocietyPhysical Review X2160-33082019-05-019202103310.1103/PhysRevX.9.021033Entanglement Spreading in a Minimal Model of Maximal Many-Body Quantum ChaosBruno BertiniPavel KosTomaž ProsenThe 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.http://doi.org/10.1103/PhysRevX.9.021033 |
| spellingShingle | Bruno Bertini Pavel Kos Tomaž Prosen Entanglement Spreading in a Minimal Model of Maximal Many-Body Quantum Chaos Physical Review X |
| title | Entanglement Spreading in a Minimal Model of Maximal Many-Body Quantum Chaos |
| title_full | Entanglement Spreading in a Minimal Model of Maximal Many-Body Quantum Chaos |
| title_fullStr | Entanglement Spreading in a Minimal Model of Maximal Many-Body Quantum Chaos |
| title_full_unstemmed | Entanglement Spreading in a Minimal Model of Maximal Many-Body Quantum Chaos |
| title_short | Entanglement Spreading in a Minimal Model of Maximal Many-Body Quantum Chaos |
| title_sort | entanglement spreading in a minimal model of maximal many body quantum chaos |
| url | http://doi.org/10.1103/PhysRevX.9.021033 |
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