Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1803.10244 · Physical review. D/Physical review. D.

Membrane theory of entanglement dynamics from holography

Márk Mezei

Published Nov 27, 2018• 65 citations
arXivHTMLPDF

Abstract

Recently, a minimal membrane description of the entanglement dynamics of large regions in generic chaotic systems was conjectured in Jonay, Huse, and Nahum (arXiv:1803.00089). Analytic results in random circuits and spin chain numerics support this theory. We show that the results found by Mezei [J. High Energy Phys. 05 (2017) 064], 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.

DOI
10.1103/physrevd.98.106025

Related papers

Bit threads and the membrane theory of entanglement dynamics

César A. Agón, Márk Mezei

Abstract Recently, an effective membrane theory was proposed that describes the “hydrodynamic” regime of the entanglement dynamics for general chaotic systems. Motivated by the new bit threads formulation of holographic entanglement entropy, given in terms of a convex optimization problem based on flow maximization, or equivalently tight packing of bit threads, we reformulate the membrane theory as a max flow problem by proving a max flow-min cut theorem. In the context of holography, we explain the relation between the max flow program dual to the membrane theory and the max flow program dual to the holographic surface extremization prescription by providing an explicit map from the membrane to the bulk, and derive the former from the latter in the “hydrodynamic” regime without reference to minimal surfaces or membranes.

arXiv:1910.12909•Journal of High Energy Physics•Nov 1, 2021•21 citations

The entanglement membrane in 2d CFT: reflected entropy, RG flow, and information velocity

Hanzhi Jiang, Márk Mezei, Julio Virrueta

A bstract The time evolution of entanglement entropy in generic chaotic many-body systems has an effective description in terms of a minimal membrane, characterised by a tension function. For 2d CFTs, a degenerate tension function reproduces several results regarding the dynamics of the entropy; this stands in contrast to higher dimensions where the tension is non-degenerate. In this paper we use holography to show that, in order to correctly capture the reflected entropy in 2d CFT, one needs to add an additional degree of freedom to the membrane description. Furthermore, we show that the conventional non-degenerate membrane tension function emerges upon introducing a relevant deformation of the CFT, dual to a planar BTZ black hole with scalar hair and with an interior Kasner universe. Finally, we also study the membrane description for reflected entropy and information velocity [1] in higher dimensions.

arXiv:2411.16542•Journal of High Energy Physics•Jun 12, 2025•4 citations

On entanglement dynamics in holographic theories

Hanzhi Jiang

Entanglement entropy (EE) is a concept of paramount importance in modern theoretical physics. Nevertheless, calculating EE in generic interacting theories with non-trivial time dependence is notoriously difficult. In this thesis, we address the real-time dynamics of EE in certain strongly-coupled quantum field theories (QFT) using the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence. We first study the time evolution of EE in an exactly solvable model of two-dimensional CFT with an inhomogeneous sine-square deformation (SSD). We argue that the non-trivial time evolutions driven by the SSD Hamiltonian can be regarded as changing the foliations of spacetime. Remarkably, this leads to the presence of new horizons in the dual three-dimensional bulk. We then compute the EE in SSD CFT using holography and found agreement with CFT results in all comparable cases. Afterwards, we proceed to entanglement dynamics in generic chaotic quantum many-body systems. In the limit of large subsystems and late times, entanglement dynamics is believed to be described by an entanglement membrane effective theory. For 2d CFTs, a degenerate tension function reproduces several results regarding the dynamics of the entropy; this stands in contrast to higher dimensions where the tension is non-degenerate. We use holography to show that, in order to correctly capture the reflected entropy in 2d CFT, one needs to add an additional degree of freedom to the membrane description. Furthermore, we show that the conventional non-degenerate membrane tension function emerges upon introducing a relevant deformation to the CFT, dual to a planar Banados-Teitelboim-Zanelli (BTZ) black hole with scalar hair and with an interior Kasner universe. Subsequently, we establish a membrane effective theory for the dynamics of reflected entropy in higher dimensions. Lastly, we apply the membrane theories for reflected entropy to study the time evolution of multiparty entanglement signals. We found that scrambling dynamics generate multiparty entanglement with rich structures.

•Jan 1, 2025•0 citations

Exploring the membrane theory of entanglement dynamics

Márk Mezei, Julio Virrueta

Abstract Recently an effective membrane theory valid in a “hydrodynamic limit” was proposed to describe entanglement dynamics of chaotic systems based on results in random quantum circuits and holographic gauge theories. In this paper, we show that this theory is robust under a large set of generalizations. In generic quench protocols we find that the membrane couples geometrically to hydrodynamics, joining quenches are captured by branes in the effective theory, and the entanglement of time evolved local operators can be computed by probing a time fold geometry with the membrane. We also demonstrate that the structure of the effective theory does not change under finite coupling corrections holographically dual to higher derivative gravity and that subleading orders in the hydrodynamic expansion can be incorporated by including higher derivative terms in the effective theory.

arXiv:1912.11024•Journal of High Energy Physics•Feb 1, 2020•27 citations

Entanglement membrane in the Brownian SYK chain

Márk Mezei, Harshit Rajgadia

There is mounting evidence that entanglement dynamics in chaotic many-body quantum systems in the limit of large subsystems and long times is described by an entanglement membrane effective theory. In this paper, we derive the membrane description in a solvable chaotic large-$N$ model, the Brownian SYK chain. This model has a collective field description in terms of fermion bilinears connecting different folds of the multifold Schwinger-Keldysh path integral used to compute Rényi entropies. The entanglement membrane is a traveling wave solution of the saddle point equations governing these collective fields. The entanglement membrane is characterised by a velocity $v$ and a membrane tension ${\cal E}(v)$ that we calculate. We find that the membrane has finite width for $v<v_B$ (the butterfly velocity), however for $v > v_B$, the membrane splits into two wave fronts, each moving with the butterfly velocity. Our results provide a new viewpoint on the entanglement membrane and uncover new connections between quantum information dynamics and scrambling.

hep-thCross-listedarXiv:2512.04179•Journal of High Energy Physics•Dec 5, 2025•0 citations

Coarse-grained dynamics of operator and state entanglement

Cheryne Jonay, David A. Huse, Adam Nahum

We give a detailed theory for the leading coarse-grained dynamics of entanglement entropy of states and of operators in generic short-range interacting quantum many-body systems. This includes operators spreading under Heisenberg time evolution, which we find are much less entangled than "typical" operators of the same spatial support. Extending previous conjectures based on random circuit dynamics, we provide evidence that the leading-order entanglement dynamics of a given chaotic system are determined by a function $\mathcal{E}(v)$, which is model-dependent, but which we argue satisfies certain general constraints. In a minimal membrane picture, $\mathcal{E}(v)$ is the "surface tension" of the membrane and is a function of the membrane's orientation $v$ in spacetime. For one-dimensional (1D) systems this surface tension is related by a Legendre transformation to an entanglement entropy growth rate $Γ(\partial S/\partial x)$ which depends on the spatial "gradient" of the entanglement entropy $S(x,t)$ across the cut at position $x$. We show how to extract the entanglement growth functions numerically in 1D at infinite temperature using the concept of the operator entanglement of the time evolution operator, and we discuss possible universality of $\mathcal{E}$ at low temperatures. Our theoretical ideas are tested against and informed by numerical results for a quantum-chaotic 1D spin Hamiltonian. These results are relevant to the broad class of chaotic many-particle systems or field theories with spatially local interactions, both in 1D and above.

arXiv:1803.00089•Feb 28, 2018•88 citations
Recently, a minimal membrane description of the entanglement dynamics of large regions in generic chaotic systems was conjectured in Jonay, Huse, and Nahum (arXiv:1803.00089). Analytic results in random circuits and spin chain numerics support this theory. We show that the results found by Mezei [J. High Energy Phys. 05 (2017) 064], 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.
Abstract Recently, an effective membrane theory was proposed that describes the “hydrodynamic” regime of the entanglement dynamics for general chaotic systems. Motivated by the new bit threads formulation of holographic entanglement entropy, given in terms of a convex optimization problem based on flow maximization, or equivalently tight packing of bit threads, we reformulate the membrane theory as a max flow problem by proving a max flow-min cut theorem. In the context of holography, we explain the relation between the max flow program dual to the membrane theory and the max flow program dual to the holographic surface extremization prescription by providing an explicit map from the membrane to the bulk, and derive the former from the latter in the “hydrodynamic” regime without reference to minimal surfaces or membranes.
A bstract The time evolution of entanglement entropy in generic chaotic many-body systems has an effective description in terms of a minimal membrane, characterised by a tension function. For 2d CFTs, a degenerate tension function reproduces several results regarding the dynamics of the entropy; this stands in contrast to higher dimensions where the tension is non-degenerate. In this paper we use holography to show that, in order to correctly capture the reflected entropy in 2d CFT, one needs to add an additional degree of freedom to the membrane description. Furthermore, we show that the conventional non-degenerate membrane tension function emerges upon introducing a relevant deformation of the CFT, dual to a planar BTZ black hole with scalar hair and with an interior Kasner universe. Finally, we also study the membrane description for reflected entropy and information velocity [1] in higher dimensions.
Entanglement entropy (EE) is a concept of paramount importance in modern theoretical physics. Nevertheless, calculating EE in generic interacting theories with non-trivial time dependence is notoriously difficult. In this thesis, we address the real-time dynamics of EE in certain strongly-coupled quantum field theories (QFT) using the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence. We first study the time evolution of EE in an exactly solvable model of two-dimensional CFT with an inhomogeneous sine-square deformation (SSD). We argue that the non-trivial time evolutions driven by the SSD Hamiltonian can be regarded as changing the foliations of spacetime. Remarkably, this leads to the presence of new horizons in the dual three-dimensional bulk. We then compute the EE in SSD CFT using holography and found agreement with CFT results in all comparable cases. Afterwards, we proceed to entanglement dynamics in generic chaotic quantum many-body systems. In the limit of large subsystems and late times, entanglement dynamics is believed to be described by an entanglement membrane effective theory. For 2d CFTs, a degenerate tension function reproduces several results regarding the dynamics of the entropy; this stands in contrast to higher dimensions where the tension is non-degenerate. We use holography to show that, in order to correctly capture the reflected entropy in 2d CFT, one needs to add an additional degree of freedom to the membrane description. Furthermore, we show that the conventional non-degenerate membrane tension function emerges upon introducing a relevant deformation to the CFT, dual to a planar Banados-Teitelboim-Zanelli (BTZ) black hole with scalar hair and with an interior Kasner universe. Subsequently, we establish a membrane effective theory for the dynamics of reflected entropy in higher dimensions. Lastly, we apply the membrane theories for reflected entropy to study the time evolution of multiparty entanglement signals. We found that scrambling dynamics generate multiparty entanglement with rich structures.
Abstract Recently an effective membrane theory valid in a “hydrodynamic limit” was proposed to describe entanglement dynamics of chaotic systems based on results in random quantum circuits and holographic gauge theories. In this paper, we show that this theory is robust under a large set of generalizations. In generic quench protocols we find that the membrane couples geometrically to hydrodynamics, joining quenches are captured by branes in the effective theory, and the entanglement of time evolved local operators can be computed by probing a time fold geometry with the membrane. We also demonstrate that the structure of the effective theory does not change under finite coupling corrections holographically dual to higher derivative gravity and that subleading orders in the hydrodynamic expansion can be incorporated by including higher derivative terms in the effective theory.
There is mounting evidence that entanglement dynamics in chaotic many-body quantum systems in the limit of large subsystems and long times is described by an entanglement membrane effective theory. In this paper, we derive the membrane description in a solvable chaotic large-NNN model, the Brownian SYK chain. This model has a collective field description in terms of fermion bilinears connecting different folds of the multifold Schwinger-Keldysh path integral used to compute Rényi entropies. The entanglement membrane is a traveling wave solution of the saddle point equations governing these collective fields. The entanglement membrane is characterised by a velocity vvv and a membrane tension E(v){\cal E}(v)E(v) that we calculate. We find that the membrane has finite width for v<vBv<v_Bv<vB​ (the butterfly velocity), however for v>vBv > v_Bv>vB​, the membrane splits into two wave fronts, each moving with the butterfly velocity. Our results provide a new viewpoint on the entanglement membrane and uncover new connections between quantum information dynamics and scrambling.
We give a detailed theory for the leading coarse-grained dynamics of entanglement entropy of states and of operators in generic short-range interacting quantum many-body systems. This includes operators spreading under Heisenberg time evolution, which we find are much less entangled than "typical" operators of the same spatial support. Extending previous conjectures based on random circuit dynamics, we provide evidence that the leading-order entanglement dynamics of a given chaotic system are determined by a function E(v)\mathcal{E}(v)E(v), which is model-dependent, but which we argue satisfies certain general constraints. In a minimal membrane picture, E(v)\mathcal{E}(v)E(v) is the "surface tension" of the membrane and is a function of the membrane's orientation vvv in spacetime. For one-dimensional (1D) systems this surface tension is related by a Legendre transformation to an entanglement entropy growth rate Γ(∂S/∂x)Γ(\partial S/\partial x)Γ(∂S/∂x) which depends on the spatial "gradient" of the entanglement entropy S(x,t)S(x,t)S(x,t) across the cut at position xxx. We show how to extract the entanglement growth functions numerically in 1D at infinite temperature using the concept of the operator entanglement of the time evolution operator, and we discuss possible universality of E\mathcal{E}E at low temperatures. Our theoretical ideas are tested against and informed by numerical results for a quantum-chaotic 1D spin Hamiltonian. These results are relevant to the broad class of chaotic many-particle systems or field theories with spatially local interactions, both in 1D and above.