Cage-Net Fracton Models

Journal Article · Wed Apr 17 00:00:00 EDT 2019 · Physical Review. X

DOI:https://doi.org/10.1103/PhysRevX.9.021010· OSTI ID:1507464

Prem, Abhinav; Huang, Sheng-Jie; Song, Hao; Hermele, Michael

We introduce a class of gapped three-dimensional models, dubbed “cage-net fracton models,” which host immobile fracton excitations in addition to non-Abelian particles with restricted mobility. Starting from layers of two-dimensional string-net models, whose spectrum includes non-Abelian anyons, we condense extended one-dimensional “flux strings” built out of pointlike excitations. Flux-string condensation generalizes the concept of anyon condensation familiar from conventional topological order and allows us to establish properties of the fracton-ordered (equivalently, flux-string-condensed) phase, such as its ground-state wave function and spectrum of excitations. Through the examples of doubled-Ising and ${\mathrm{SU}\left(2\right)}_k$ cage-net models, we demonstrate the existence of strictly immobile Abelian fractons and of non-Abelian particles restricted to move only along one dimension. In the doubled-Ising cage-net model, we show that these restricted-mobility non-Abelian excitations are a fundamentally three-dimensional phenomenon, as they cannot be understood as bound states among two-dimensional non-Abelian anyons and Abelian particles. We further show that the ground-state wave function of such phases can be understood as a fluctuating network of extended objects—cages—and strings, which we dub a cage-net condensate. Besides having implications for topological quantum computation in three dimensions, our work may also point the way towards more general insights into quantum phases of matter with fracton order.

• Sponsoring Organization: USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
• Grant/Contract Number: SC0014415
• OSTI ID: 1507464
• Alternate ID(s): OSTI ID: 1612180
• Journal Information: Physical Review. X, Journal Name: Physical Review. X Journal Issue: 2 Vol. 9; ISSN PRXHAE; ISSN 2160-3308
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English

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