Topological entanglement entropy of fracton stabilizer codes

Journal article

Entanglement entropy provides a powerful characterization of two-dimensional gapped topolog- ical 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 that lack a TQFT description. 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 archety- pal fracton models - the `X-cube model' and `Haah's code' - and demonstrate the existence of a non-local contribution that scales linearly in subsystem size. We show via Schrieffer-Wolff transfor- mations that this piece of the entanglement entropy 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.

Authors: Ma, H; Schmitz, A; Parameswaran, S; Hermele, M; Nandkishore, R

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: American Physical Society
• Journal: Physical Review B
• Volume: 97
• Issue: 12
• Pages: 1-16
• Publication date: 2018-01-01
• Acceptance date: 2018-02-14
• DOI: 10.1103/PhysRevB.97.125101
• EISSN: 2469-9969
• ISSN: 2469-9950