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

Excitations in (3+1)D topologically ordered phases have very rich structures.(3+1)D topological phases support both point-like and string-like excitations,and in particular the loop (closed string) excitations may admit knotted andlinked structures. In this work, we ask the question how different types oftopological excitations contribute to the entanglement entropy, oralternatively, can we use the entanglement entropy to detect the structure ofexcitations, and further obtain the information of the underlying topologicalorders? We are mainly interested in (3+1)D topological orders that can berealized in Dijkgraaf-Witten gauge theories, which are labeled by a finitegroup $G$ and its group 4-cocycle $\omega\in\mathcal{H}^4[G;U(1)]$ up to groupautomorphisms. We find that each topological excitation contributes a universalconstant $\ln d_i$ to the entanglement entropy, where $d_i$ is the quantumdimension that depends on both the structure of the excitation and the data$(G,\,\omega)$. The entanglement entropy of the excitations of thelinked/unlinked topology can capture different information of the DW theory$(G,\,\omega)$. In particular, the entanglement entropy introduced by Hopf-linkloop excitations can distinguish certain group 4-cocycles $\omega$ from theothers.

Entanglement entropy of (3+1)D topological orders with excitations