Hyperbolic Fracton Models: Bridging AdS/CFT and Self-Correcting Code

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• Prof. Han YAN (Tokyo)
• Friday 07 November 2025, 14:00-15:30
• Seminar Room 2 - D2.002.

If you have a question about this talk, please contact Bo Peng.

Fracton models—many-body systems whose excitations can only appear in restricted multipole configurations—have emerged as a fertile ground for exploring connections between quantum information, topological phases of matter, and exotic dynamics. In this talk, I will introduce a class of classical fracton models defined on hyperbolic lattices, i.e., lattices embedded in spaces of constant negative curvature. These models exhibit two particularly intriguing features:

1. Holographic behavior: a subclass of the models possesses subsystem symmetries organized by fractal trees and, in the low-energy limit, realizes infinitely many copies of Zabrodin’s p-adic model of AdS/CFT. Remarkably, these models naturally reproduce key features of holography, including the Ryu-Takayanagi relation for mutual information and Rindler reconstruction.

2. Self-correcting memory: unlike conventional flat-space fracton models, where the energy barrier for moving excitations grows at most logarithmically with linear system size L, in the hyperbolic setting, the barrier grows exponentially with distance and algebraically with system size. This scaling renders the system intrinsically robust against local perturbations, providing an example of a self-correcting classical memory. Together, these results suggest that hyperbolic fracton models provide an intriguing framework for exploring emergent holography and robust information storage in strongly constrained many-body systems, and perhaps a deeper connection between the two.

References:

H Yan. PRB 99 (15), 155126, PRB 100 (24), 245138, PRB 102 (16), 161119,

H Yan, CB Jepsen, Y Oz JHEP2 025 (8), 1-19

This talk is part of the Theory of Condensed Matter series.

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