# Deciphering the nonlocal entanglement entropy of fracton topological orders

## TL;DR

This paper investigates the nonlocal entanglement entropy in fracton topological orders, deriving bounds that reveal geometry-dependent properties and potential distinctions from conventional topological phases.

## Contribution

It introduces a lower bound for nonlocal entanglement entropy applicable to fracton models, extending understanding beyond traditional topological quantum field theory descriptions.

## Key findings

- Lower bound applies to Abelian stabilizer models including fractons and topological orders.
- Nonlocal entanglement entropy can be geometry-dependent and extensive in fracton models.
- The lower bound remains stable under local perturbations.

## Abstract

The ground states of topological orders condense extended objects and support topological excitations. This nontrivial property leads to nonzero topological entanglement entropy $S_{topo}$ for conventional topological orders. Fracton topological order is an exotic class of models which is beyond the description of TQFT. With some assumptions about the condensates and the topological excitations, we derive a lower bound of the nonlocal entanglement entropy $S_{nonlocal}$ (a generalization of $S_{topo}$). The lower bound applies to Abelian stabilizer models including conventional topological orders as well as type \Rom{1} and type \Rom{2} fracton models, and it could be used to distinguish them. For fracton models, the lower bound shows that $S_{nonlocal}$ could obtain geometry-dependent values, and $S_{nonlocal}$ is extensive for certain choices of subsystems, including some choices which always give zero for TQFT. The stability of the lower bound under local perturbations is discussed.