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1. Entanglement phase structure of a holographic BCFT in a black hole background

   https://doi.org/10.1007/JHEP05(2022)153  

   Geng, Hao; Karch, Andreas; Perez-Pardavila, Carlos; Raju, Suvrat; Randall, Lisa; Riojas, Marcos; Shashi, Sanjit (May 2022, Journal of High Energy Physics)

   A<sc>bstract</sc> We compute holographic entanglement entropy for subregions of a BCFT thermal state living on a nongravitating black hole background. The system we consider is doubly holographic and dual to an eternal black string with an embedded Karch-Randall brane that is parameterized by its angle. Entanglement islands are conventionally expected to emerge at late times to preserve unitarity at finite temperature, but recent calculations at zero temperature have shown such islands do not exist when the brane lies below a critical angle. When working at finite temperature in the context of a black string, we find that islands exist even when the brane lies below the critical angle. We note that although these islands exist when they are needed to preserve unitarity, they are restricted to a finite connected region on the brane which we call the atoll. Depending on two parameters — the size of the subregion and the brane angle — the entanglement entropy either remains constant in time or follows a Page curve. We discuss this rich phase structure in the context of bulk reconstruction. 

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2. On the spread of entanglement at finite cutoff

   https://doi.org/10.1007/JHEP05(2023)213  

   Coleman, Evan; Soni, Ronak M.; Yang, Sungyeon (May 2023, Journal of High Energy Physics)

   A<sc>bstract</sc> We study how entanglement spreads in the boundary duals of finite-cutoff three-dimensional theories with positive, negative and zero cosmological constant, the$$ T\overline{T} $$ $T\overline{T}$+ Λ₂two-dimensional theories. We first study the Hawking-Page transition in all three cases, and find that there is a transition in all three scenarios at the temperature where the lengths of the two cycles of the torus are the same. We then study the entanglement entropy in the thermofield double states above the Hawking-Page transition, of regions symmetrically placed on the two boundaries. We consider the case where the region is one interval on each side, and the case where it is two intervals on each side. We give an entanglement tsunami interpretation of the time-evolution of the entanglement entropies. 

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3. Effective entropy of quantum fields coupled with gravity

   https://doi.org/10.1007/JHEP10(2020)052  

   Dong, Xi; Qi, Xiao-Liang; Shangnan, Zhou; Yang, Zhenbin (October 2020, Journal of High Energy Physics)

   null (Ed.)

   A bstract Entanglement entropy, or von Neumann entropy, quantifies the amount of uncertainty of a quantum state. For quantum fields in curved space, entanglement entropy of the quantum field theory degrees of freedom is well-defined for a fixed background geometry. In this paper, we propose a generalization of the quantum field theory entanglement entropy by including dynamical gravity. The generalized quantity named effective entropy, and its Renyi entropy generalizations, are defined by analytic continuation of a replica calculation. The replicated theory is defined as a gravitational path integral with multiple copies of the original boundary conditions, with a co-dimension-2 brane at the boundary of region we are studying. We discuss different approaches to define the region in a gauge invariant way, and show that the effective entropy satisfies the quantum extremal surface formula. When the quantum fields carry a significant amount of entanglement, the quantum extremal surface can have a topology transition, after which an entanglement island region appears. Our result generalizes the Hubeny-Rangamani-Takayanagi formula of holographic entropy (with quantum corrections) to general geometries without asymptotic AdS boundary, and provides a more solid framework for addressing problems such as the Page curve of evaporating black holes in asymptotic flat spacetime. We apply the formula to two example systems, a closed two-dimensional universe and a four-dimensional maximally extended Schwarzchild black hole. We discuss the analog of the effective entropy in random tensor network models, which provides more concrete understanding of quantum information properties in general dynamical geometries. We show that, in absence of a large boundary like in AdS space case, it is essential to introduce ancilla that couples to the original system, in order for correctly characterizing quantum states and correlation functions in the random tensor network. Using the superdensity operator formalism, we study the system with ancilla and show how quantum information in the entanglement island can be reconstructed in a state-dependent and observer-dependent map. We study the closed universe (without spatial boundary) case and discuss how it is related to open universe. 

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4. Entropy of radiation with dynamical gravity

   https://doi.org/10.1007/JHEP05(2023)038  

   Perez-Pardavila, Carlos (May 2023, Journal of High Energy Physics)

   A<sc>bstract</sc> We compute the subregion entanglement entropy for a doubly holographic black string model. This system consists of a non-gravitating bath and a gravitating brane, where we incorporate dynamic gravity by adding a DGP term. This opens up a new parameter directly extending previous work and raises an important question about unitarity. In this note we analyse which theories in this big parameter space, will have unitary entropy evolution, in particular, we will distinguish which of those will follow a Page curve. 

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5. Generalized free cumulants for quantum chaotic systems

   https://doi.org/10.1007/JHEP09(2024)066  

   Jindal, Siddharth; Hosur, Pavan (September 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> The eigenstate thermalization hypothesis (ETH) is the leading conjecture for the emergence of statistical mechanics in generic isolated quantum systems and is formulated in terms of the matrix elements of operators. An analog known as the ergodic bipartition (EB) describes entanglement and locality and is formulated in terms of the components of eigenstates. In this paper, we significantly generalize the EB and unify it with the ETH, extending the EB to study higher correlations and systems out of equilibrium. Our main result is a diagrammatic formalism that computes arbitrary correlations between eigenstates and operators based on a recently uncovered connection between the ETH and free probability theory. We refer to the connected components of our diagrams as generalized free cumulants. We apply our formalism in several ways. First, we focus on chaotic eigenstates and establish the so-called subsystem ETH and the Page curve as consequences of our construction. We also improve known calculations for thermal reduced density matrices and comment on an inherently free probabilistic aspect of the replica approach to entanglement entropy previously noticed in a calculation for the Page curve of an evaporating black hole. Next, we turn to chaotic quantum dynamics and demonstrate the ETH as a sufficient mechanism for thermalization, in general. In particular, we show that reduced density matrices relax to their equilibrium form and that systems obey the Page curve at late times. We also demonstrate that the different phases of entanglement growth are encoded in higher correlations of the EB. Lastly, we examine the chaotic structure of eigenstates and operators together and reveal previously overlooked correlations between them. Crucially, these correlations encode butterfly velocities, a well-known dynamical property of interacting quantum systems. 

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