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

TL;DR

This paper extends the Hyperbolic Fracton Model to generic tessellations, revealing complex subsystem symmetries and fracton behaviors while confirming the persistence of holographic features across diverse geometries.

Contribution

It generalizes the hyperbolic fracton model beyond the original tessellation, analyzing its properties and confirming holographic correspondence in more intricate geometries.

Findings

Ground-state degeneracy generated recursively via inflation rule

Fracton excitations exhibit exponential and algebraic growth patterns

Holographic features like subregion duality and Ryu-Takayanagi formula remain valid

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.