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

Symmetry fractionalization (SF) on topological excitations is one of the mostremarkable quantum phenomena in topological orders with symmetry, i.e.,symmetry-enriched topological phases. While much progress has beentheoretically and experimentally made in 2D, the understanding on SF in 3D isfar from complete. A long-standing challenge is to understand SF on loopliketopological excitations which are spatially extended objects. In this work, weconstruct a powerful topological-field-theoretical framework approach for 3Dtopological orders, which leads to a systematic characterization andclassification of SF. For systems with Abelian gauge groups ($G_g$) and Abeliansymmetry groups ($G_s$), we successfully establish equivalence classes thatlead to a finite number of patterns of SF, although there are notoriouslyinfinite number of Lagrangian-descriptions of the system. We computetopologically distinct types of fractional symmetry charges carried byparticles. Then, for each type, we compute topologically distinct statisticalphases of braiding processes among loop excitations and external symmetryfluxes. As a result, we are able to unambiguously list all physical observablesfor each pattern of SF. We present detailed calculations on many concreteexamples. As an example, we find that the SF in an untwisted$\mathbb{Z}_2\times \mathbb{Z}_2$ topological order with $\mathbb{Z}_2$symmetry is classified by $ (\mathbb{Z}_2)^6\oplus (\mathbb{Z}_2)^2\oplus(\mathbb{Z}_2)^2\oplus (\mathbb{Z}_2)^2$. If the topological order is twisted,the classification reduces to $(\mathbb{Z}_2)^6$ in which particle excitationsalways carry integer charge. Pure algebraic formalism of the classification isgiven by: $ \bigoplus_{\nu_i} \mathcal H^4 ( G_g\leftthreetimes_{\nu_i}G_s, U(1)) /\Gamma_\omega ({\nu_i}) \,$. Several future directions are proposed.

Fractionalizing Global Symmetry on Looplike Topological Excitations