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

Abelian Chern-Simons theory, characterized by the so-called $K$ matrix, hasbeen quite successful in characterizing and classifying Abelian fractionalquantum hall effect (FQHE) as well as symmetry protected topological (SPT)phases, especially for bosonic SPT phases. However, there are still somepuzzles in dealing with fermionic SPT(fSPT) phases. In this paper, we utilizethe Abelian Chern-Simons theory to study the fSPT phases protected by arbitraryAbelian total symmetry $G_f$. Comparing to the bosonic SPT phases, fSPT phaseswith Abelian total symmetry $G_f$ has three new features: (1) it may supportgapless majorana fermion edge modes, (2) some nontrivial bosonic SPT phases maybe trivialized if $G_f$ is a nontrivial extention of bosonic symmetry $G_b$over $\mathbb{Z}_2^f$, (3) certain intrinsic fSPT phases can only be realizedin interacting fermionic system. We obtain edge theories for various fSPTphases, which can also be regarded as conformal field theories (CFT) withproper symmetry anomaly. In particular, we discover the construction ofLuttinger liquid edge theories with central charge $n-1$ for Type-III bosonicSPT phases protected by $(\mathbb{Z}_n)^3$ symmetry and the Luttinger liquidedge theories for intrinsically interacting fSPT protected by unitary Abeliansymmetry. The ideas and methods used here might be generalized to derive theedge theories of fSPT phases with arbitrary unitary finite Abelian totalsymmetry $G_f$.

Edge theories of 2D fermionic symmetry protected topological phases protected by unitary Abelian symmetries