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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The quantum spin Hall effect shares many similarities (and some importantdifferences) with the quantum Hall effect for the electric charge. As with thequantum (electric charge) Hall effect, there exists a correspondence betweenbulk and boundary physics that allows to characterize the quantum spin Halleffect in diverse and complementary ways. In this paper, we derive from thenetwork model that encodes the quantum spin Hall effect, the so-called Z_2network model, a Dirac Hamiltonian in two dimensions. In the clean limit ofthis Dirac Hamiltonian, we show that the bulk Kane-Mele Z_2 invariant isnothing but the SU(2) Wilson loop constructed from the SU(2) Berry connectionof the occupied Dirac-Bloch single-particle states. In the presence ofdisorder, the non-linear sigma model (NLSM) that is derived from this DiracHamiltonian describes a metal-insulator transition in the standardtwo-dimensional symplectic universality class. In particular, we show that thefermion doubling prevents the presence of a topological term in the NLSM thatwould change the universality class of the ordinary two-dimensional symplecticmetal-insulator transition. This analytical result is fully consistent with ourprevious numerical studies of the bulk critical exponents at themetal-insulator transition encoded by the Z_2 network model. Finally, weimprove the quality and extend the numerical study of boundary multifractalityin the Z_2 topological insulator. We show that the hypothesis oftwo-dimensional conformal invariance at the metal-insulator transition isverified within the accuracy of our numerical results.

The Z_2 network model for the quantum spin Hall effect: two-dimensional Dirac fermions, topological quantum numbers, and corner multifractality