arXiv subjects

Haocheng Zhong

Publications and source records attributed to Haocheng Zhong.

11 recordsLinked to original sources

arXiv2026

A Geodesic Route toward Holography beyond AdS: Tessellating the Schwarzschild Black Hole

In vacuum anti-de Sitter (AdS) space, the geometry admits a perfect tessellation by a geodesic network. This tessellation characterizes the background exactly, and a partial entanglement entropy (PEE) tensor-network toy model of AdS/CFT can be defined on it. It has so far been unclear whether this construction can be extended beyond vacuum AdS. In this paper we take the first step in this direction. We show that the exterior region of the Schwarzschild black hole and its Einstein--Rosen bridge are perfectly tessellated by a specific geodesic gas emitted from the boundary, so that Crofton reconstruction holds in these regions. We then prove that such a geodesic tessellation and the Crofton reconstruction it defines extend to more generic Riemannian manifolds. This allows us to construct a PEE tensor-network model of holographic duality on more generic geometric backgrounds. In the case of the PEE tensor-network model for the Schwarzschild background, we can concretely realize the Bekenstein--Hawking entropy, the Ryu--Takayanagi formula and the ER=EPR proposal. Our approach opens a new route towards holographic toy models beyond AdS/CFT.

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arXiv2026

Semiclassical algebraic reconstruction for type III algebras

In this work, we address the unresolved type III cases of the algebraic reconstruction theorem by integrating crossed product algebras and semiclassical approximations. We first derive that the relative entropy in crossed product algebras factorizes into contributions from the original algebra and observer wavefunctions. By constructing ``holographic'' crossed product algebras for ``bulk'' and ``boundary'' type III factors, we extend the algebraic reconstruction theorem to include the algebraic Ryu-Takayanagi (RT) formula semiclassically, which provides a complete algebraic description of the reconstruction theorem, as an intrinsic framework for the algebraic version of bulk-boundary correspondences in holographic duality.

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arXiv2026

Holographic Tensor Networks as Tessellations of Geometry

Holographic tensor networks serve as toy models for the Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence, capturing many of its essential features in a concrete manner. However, existing holographic tensor network models remain far from a complete theory of quantum gravity. A key obstacle is their discrete structure, which only approximates the semi-classical geometry of gravity in a qualitative sense. In \cite{Lin:2024dho}, it was shown that a network of partial-entanglement-entropy (PEE) threads, which are bulk geodesics with a specific density distribution, generates a perfect tessellation of AdS space. Moreover, such PEE-network tessellations can be constructed for more highly symmetric geometries using the Crofton formula. In this paper, we assign a quantum state to each vertex in the PEE network and develop several holographic tensor network models: (1) the factorized PEE tensor network, which takes the form of a tensor product of EPR pairs; (2) the HaPPY-like PEE tensor network constructed from perfect tensors; and (3) the random PEE tensor network. In all these models, we reproduce the exact Ryu-Takayanagi formula by showing that the minimal number of cuts along a homologous surface in the network exactly equals the area of that surface.

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arXiv2026

An algebraic description of the Page transition

In this work, we develop an algebraic description of the Page transition, a key feature in black hole evaporation where the entropy of Hawking radiation follows a unitary Page curve instead of monotonically increasing. By applying concepts from approximate quantum error correction with complementary recovery, we characterize the Page transition as a phase transition in channel recovery. We then generalize the description to infinite-dimensional settings using algebraic relative entropy, which remains valid even in type III factors. For type I/II factors, explicit probes based on relative entropy differences are derived, serving as indicators for the transition at the Page time.

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arXiv2025

Adding the algebraic Ryu-Takayanagi formula to the algebraic reconstruction theorem

A huge progress in studying holographic theories is that holography can be interpreted via the quantum error correction, which makes equal the entanglement wedge reconstruction, the Jafferis-Lewkowycz-Maldacena-Suh formula, the radial commutativity and the Ryu-Takayanagi formula. We call the equivalence the reconstruction theorem, whose infinite-dimensional generalization via algebraic language was believed to exclude the algebraic version of the Ryu-Takayanagi formula. However, recent developments regarding gravitational algebras have shown that the inclusion of the algebraic Ryu-Takayanagi formula is plausible. In this letter, we prove that such inclusion holds for the cases of type I/II factors, which are expected to describe holographic theories.

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arXiv2025

Timelike and gravitational anomalous entanglement from the inner horizon

In the context of the AdS$_3$/CFT$_2$, the boundary causal development and the entanglement wedge of any boundary spacelike interval can be mapped to a thermal CFT$_2$ and a Rindler $\widetilde{\text{AdS}_3}$ respectively via certain boundary and bulk Rindler transformations. Nevertheless, the Rindler mapping is not confined in the entanglement wedges. While the outer horizon of the Rindler $\widetilde{\text{AdS}_3}$ is mapped to the RT surface, we also identify the pre-image of the inner horizon in the original AdS$_3$, which we call the inner RT surface. In this paper we give some new physical interpretation for the inner RT surface. First, the inner RT surface breaks into two pieces which anchor on the two tips of the causal development. Furthermore, we can take the two tips as the endpoints of a certain timelike interval and the inner RT surface is exactly the spacelike geodesic that represents the real part of the so-called holographic timelike entanglement entropy (HTEE). We also identify a timelike geodesic at boundary of the extended entanglement wedge, which represents the imaginary part of the HTEE. Second, in the duality between the topological massive gravity (TMG) and gravitational anomalous CFT$_2$, the entanglement entropy and the mixed state correlation that is dual to the entanglement wedge cross section (EWCS) receive correction from the Chern-Simons term in the TMG. We find that, the correction to the holographic entanglement entropy can be reproduced by the area of the inner RT surface with a proper regulation, while the mixed state correlation can be represented by the saddle geodesic chord connecting the two pieces of the inner RT surface of the mixed state we consider, which we call the inner EWCS. The equivalence between the twist on the RT surface and the length of inner RT surface is also discussed.

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arXiv2025

Probing the Page transition via approximate quantum error correction

In recent years, there is a huge progress in understanding the black hole information problem, and the key is that the black hole entropy of radiation should be calculated by the island formula, which describes the Page curve to ensure the unitarity of black hole evaporation. In the paper, we find that the black hole evaporation interpreted by the island formula can be understood in the language of approximate quantum error correction. Furthermore, the Page transition, as a special property of the Page curve, should be understood as the property of approximate quantum error correction itself, i.e. a general class of quantum systems under certain conditions from approximate quantum error correction can also exhibit phenomenon similar to the Page transition.

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arXiv2024

CycleNet: Enhancing Time Series Forecasting through Modeling Periodic Patterns

The stable periodic patterns present in time series data serve as the foundation for conducting long-horizon forecasts. In this paper, we pioneer the exploration of explicitly modeling this periodicity to enhance the performance of models in long-term time series forecasting (LTSF) tasks. Specifically, we introduce the Residual Cycle Forecasting (RCF) technique, which utilizes learnable recurrent cycles to model the inherent periodic patterns within sequences, and then performs predictions on the residual components of the modeled cycles. Combining RCF with a Linear layer or a shallow MLP forms the simple yet powerful method proposed in this paper, called CycleNet. CycleNet achieves state-of-the-art prediction accuracy in multiple domains including electricity, weather, and energy, while offering significant efficiency advantages by reducing over 90% of the required parameter quantity. Furthermore, as a novel plug-and-play technique, the RCF can also significantly improve the prediction accuracy of existing models, including PatchTST and iTransformer. The source code is available at: https://github.com/ACAT-SCUT/CycleNet.

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arXiv2024

Partial entanglement entropy threads in island phase

In the context of AdS/CFT, it was recently proposed that the boundary partial entanglement entropy structure can be represented by the so-called partial entanglement entropy (PEE) threads in the AdS bulk, which are bulk geodesics with the density determined by the boundary PEE structure \cite{Lin:2023rbd,Lin:2024dho}. In Poincaré AdS space, it was shown that the PEE threads cover the AdS space uniformly, such that the number of intersections between any bulk surface and the bulk PEE threads is always given by the area of the surface divided by 4G. In this paper, we investigate the configurations of PEE threads when the boundary state is in island phase. The island phase was studied in the context of the holographic Weyl transformed CFT$_2$, which has been shown to capture all the main features of AdS/BCFT. Compared with AdS$_3$/CFT$_2$, in island phase instead of modifying the distribution of the bulk PEE threads, we should replace the boundary points with the corresponding cutoff spheres. Then the two-point and four-point functions of twist operators can be reproduced by identifying the bulk homologous surfaces anchored on the corresponding cutoff spheres that has the minimal number of intersections with the bulk PEE threads. This gives us a better understanding about the PEE structure in island phase and reproduces the island formula for entanglement entropy by allowing homologous surfaces to anchor on any cutoff surfaces. Furthermore, it gives a demonstration for the two basic proposals and a better understanding for the entanglement contribution that makes the foundation to compute the balanced partial entanglement entropy (BPE) \cite{Basu:2023wmv} which reproduces the entanglement wedge cross-section in island phase.

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arXiv2022

Covariant entanglement wedge cross-section, balanced partial entanglement and gravitational anomalies

The balanced partial entanglement (BPE) was observed to give the reflected entropy and the entanglement wedge cross-section (EWCS) for various mixed states in different theories \cite{Wen:2021qgx,Camargo:2022mme}. It can be calculated in different purifications, and is conjectured to be independent from purifications. In this paper we calculate the BPE and the EWCS in generic covariant scenarios in two-dimensional CFTs with and without gravitational anomalies, and find that they coincide with the reflected entropy. In covariant configurations we determine the partition for the purifying system with the help of the gravitational anomalies, and we extend our discussion to topological massive gravity (TMG). We give the first prescription to evaluate the entropy quantity associated to the EWCS beyond Einstein gravity, i.e. the correction to the EWCS from the Chern-Simons term in TMG. Apart from the gravity theory and geometry, further input from the mixed state should be taken into account.

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arXiv2022

Balanced Partial Entanglement and Mixed State Correlations

Recently in Ref.\cite{Wen:2021qgx}, one of the authors introduced the balanced partial entanglement (BPE), which has been proposed to be dual to the entanglement wedge cross-section (EWCS). In this paper, we explicitly demonstrate that the BPE could be considered as a proper measure of the total intrinsic correlation between two subsystems in a mixed state. The total correlation includes certain crossing correlations which are minimized on some balance conditions. By constructing a class of purifications from Euclidean path-integrals, we find that the balanced crossing correlations show universality and can be considered as the generalization of the Markov gap for canonical purification. We also test the relation between the BPE and the EWCS in three-dimensional asymptotically flat holography. We find that the balanced crossing correlation vanishes for the field theory invariant under BMS$_3$ symmetry (BMSFT) and dual to the Einstein gravity, indicating the possibility of a perfect Markov recovery. We further elucidate these crossing correlations as a signature of tripartite entanglement and explain their interpretation in both AdS and non-AdS holography.

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