English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We study gapped boundaries of Abelian type-I fracton systems in three spatialdimensions. Using the X-cube model as our motivating example, we give aconjecture, with partial proof, of the conditions for a boundary to be gapped.In order to state our conjecture, we use a precise definition of fractonbraiding and show that bulk braiding of fractons has several features that makeit \textit{insufficient} to classify gapped boundaries. Most notable amongthese is that bulk braiding is sensitive to geometry and is "nonreciprocal,"that is, braiding an excitation $a$ around $b$ need not yield the same phase asbraiding $b$ around $a$. Instead, we define fractonic "boundary braiding,"which resolves these difficulties in the presence of a boundary. We thenconjecture that a boundary of an Abelian fracton system is gapped if and onlyif a "boundary Lagrangian subgroup" of excitations is condensed at theboundary, this is a generalization of the condition for a gapped boundary intwo spatial dimensions, but it relies on boundary braiding instead of bulkbraiding. We also discuss the distinctness of gapped boundaries and transitionsbetween different topological orders on gapped boundaries.

Braiding and Gapped Boundaries in Fracton Topological Phases