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arXiv:2510.25994

Hyperbolic Fracton Model, Subsystem Symmetry and Holography III: Extension to Generic Tessellations

Yosef Shokeeb, Ludovic D. C. Jaubert, Yan Han

Published Oct 29, 2025• 0 citations
arXivHTMLPDF

Abstract

We generalize the Hyperbolic Fracton Model from the $\{5,4\}$ tessellation to generic tessellations, and investigate its core properties: subsystem symmetries, fracton mobility, and holographic correspondence. While the model on the original tessellation has features reminiscent of the flat-space lattice cases, the generalized tessellations exhibit a far richer and more intricate structure. The ground-state degeneracy and subsystem symmetries are generated recursively layer-by-layer, through the inflation rule, but without a simple, uniform pattern. The fracton excitations follow exponential-in-distance and algebraic-in-lattice-size growing patterns when moving outward, and depend sensitively to the tessellation geometry, differing qualitatively from both type-I or type-II fracton model on flat lattices. Despite this increased complexity, the hallmark holographic features -- subregion duality via Rindler reconstruction, the Ryu-Takayanagi formula for mutual information, and effective black hole entropy scaling with horizon area -- remain valid. These results demonstrate that the holographic correspondence in fracton models persists in generic tessellations, and provide a natural platform to explore more intricate subsystem symmetries and fracton physics.

DOI
10.48550/arxiv.2510.25994

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We generalize the Hyperbolic Fracton Model from the {5,4}\{5,4\}{5,4} tessellation to generic tessellations, and investigate its core properties: subsystem symmetries, fracton mobility, and holographic correspondence. While the model on the original tessellation has features reminiscent of the flat-space lattice cases, the generalized tessellations exhibit a far richer and more intricate structure. The ground-state degeneracy and subsystem symmetries are generated recursively layer-by-layer, through the inflation rule, but without a simple, uniform pattern. The fracton excitations follow exponential-in-distance and algebraic-in-lattice-size growing patterns when moving outward, and depend sensitively to the tessellation geometry, differing qualitatively from both type-I or type-II fracton model on flat lattices. Despite this increased complexity, the hallmark holographic features -- subregion duality via Rindler reconstruction, the Ryu-Takayanagi formula for mutual information, and effective black hole entropy scaling with horizon area -- remain valid. These results demonstrate that the holographic correspondence in fracton models persists in generic tessellations, and provide a natural platform to explore more intricate subsystem symmetries and fracton physics.
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This report offers a comprehensive academic synthesis of the information-theoretic paradigm in fundamental physics, in which spacetime geometry, vacuum structure, and gravitational dynamics arise from the entanglement and error-correcting properties of quantum many-body systems. Beginning with the Toric Code, Color Codes, and string-net condensates, the review explains how gauge fields, fermionic statistics, and virtual particle structure emerge from stabilizer constraints and topological order. It then explores Fracton phases and subsystem symmetries as geometric substrates capable of reproducing the constraints and potentials of linearized gravity. The analysis extends into holographic quantum error correction—including MERA, the HaPPY code, and random tensor networks—to show how bulk locality, black hole entropy, and AdS geometry emerge from entanglement structure. The Hyperbolic Fracton Model is examined as a synthesis that unifies fractonic mobility constraints with holographic scaling and area-law entropy. The report supports a unified “code-theoretic” framework in which physical laws and spacetime arise from the structure of an underlying quantum code.
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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.