Cage-Net Fracton Models

TL;DR

This paper introduces cage-net fracton models, a new class of three-dimensional topologically ordered phases with immobile and restricted-mobility non-Abelian excitations, expanding understanding of fracton order and quantum phases.

Contribution

It develops the concept of flux-string condensation from layered string-net models to construct and analyze three-dimensional cage-net fracton phases with novel excitations.

Findings

Existence of strictly immobile Abelian fractons.

Presence of non-Abelian particles restricted to one-dimensional motion.

Ground state wave function as a cage-net condensate.

Abstract

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 point-like 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 SU(2)$_k$ 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 amongst 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.