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

While it is well known that three dimensional quantum many-body systems cansupport non-trivial braiding statistics between particle-like and loop-likeexcitations, or between two loop-like excitations, we argue that a morefundamental quantity is the statistical phase associated with braiding one loop$\alpha$ around another loop $\beta$, while both are linked to a third loop$\gamma$. We study this three-loop braiding in the context of$(\mathbb{Z}_N)^K$ gauge theories which are obtained by gauging a gapped,short-range entangled lattice boson model with $(\mathbb{Z}_N)^K$ symmetry. Wefind that different short-range entangled bosonic states with the same$(\mathbb{Z}_N)^K$ symmetry (i.e. different symmetry-protected topologicalphases) can be distinguished by their three-loop braiding statistics.

Braiding statistics of loop excitations in three dimensions