Topological Entanglement Entropy of Fracton Stabilizer Codes

TL;DR

This paper investigates the entanglement entropy of three-dimensional fracton models, revealing a universal topological contribution that scales linearly and is robust against perturbations, advancing understanding of fracton topological order.

Contribution

It explicitly computes entanglement entropy for fracton models and demonstrates the existence of a universal, linearly scaling topological contribution in these phases.

Findings

Topological entanglement entropy scales linearly in subsystem size for fracton models.

The topological entanglement is robust against local Hamiltonian perturbations.

Results suggest potential extension to disordered fracton systems with localization-protected order.

Abstract

Entanglement entropy provides a powerful characterization of two-dimensional gapped topological phases of quantum matter, intimately tied to their description by topological quantum field theories (TQFTs). Fracton topological orders are three-dimensional gapped topologically ordered states of matter, but the existence of a TQFT description for these phases remains an open question. We show that three-dimensional fracton phases are nevertheless characterized, at least partially, by universal structure in the entanglement entropy of their ground state wave functions. We explicitly compute the entanglement entropy for two archetypal fracton models --- the `X-cube model' and `Haah's code' --- and demonstrate the existence of a topological contribution that scales linearly in subsystem size. We show via Schrieffer-Wolff transformations that the topological entanglement of fracton models is robust against arbitrary local perturbations of the Hamiltonian. Finally, we argue that these results may be extended to characterize localization-protected fracton topological order in excited states of disordered fracton models.