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

The quantum Hall effect is studied in a spherical geometry using the Diracoperator for non-interacting fermions in a background magnetic field, which issupplied by a Wu-Yang magnetic monopole at the centre of the sphere. Wavefunctions are cross-section of a non-trivial $U(1)$ bundle, the zero pointenergy then vanishes and no perturbations can lower the energy. TheAtiyah-Singer index theorem constrains the degeneracy of the ground state.  The fractional quantum Hall effect is also studied in the composite Fermionmodel. Vortices of the statistical gauge field are supplied by Dirac stringsassociated with the monopole field. A unique ground state is attained only ifthe vortices have an even number of flux units and act to counteract thebackground field, reducing the effective field seen by the composite fermions.There is a unique gapped ground state and, for large particle numbers,fractions $\nu=\frac{1}{2 k+1}$ are recovered.

Ground state wave functions for the quantum Hall effect on a sphere and the Atiyah-Singer index theorem