Hyperbolic Fracton Model, Subsystem Symmetry, and Holography

TL;DR

This paper introduces a classical fracton model with subsystem symmetry on hyperbolic lattices as a toy model for holography, capturing key features like subregion duality and entanglement entropy scaling.

Contribution

It presents a novel classical toy model that mimics holographic properties, providing insights into quantum gravity and holography through fracton physics.

Findings

Model satisfies subregion duality

Reproduces Ryu-Takayanagi formula for mutual information

Black hole entropy scales with horizon area

Abstract

We propose that the fracton models with subsystem symmetry can be a class of toy models for the holographic principle. The discovery of the anti-de Sitter/conformal field theory correspondence as a concrete construction of holography and the subsequent developments including the subregion duality and Ryu-Takayanagi formula of entanglement entropy have revolutionized our understanding of quantum gravity and provided powerful tool sets for solving various strongly-coupled quantum field theory problems. To resolve many mysteries of holography, toy models can be very helpful. One example is the holographic tensor networks which illuminate the quantum error correcting properties of gravity in the anti-de Sitter space. In this work we discuss a classical toy model featuring subsystem symmetries and immobile fracton excitations. We show that such a model defined on the hyperbolic lattice satisfies some key properties of the holographic correspondence. The correct subregion duality and Ryu-Takayanagi formula for mutual information are established for a connected boundary region. A naively defined black hole's entropy scales as its horizon area. We also present discussions on corrections for more complicated boundary subregions, the possible generalizations of the model, and a comparison with the holographic tensor networks.