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

Frustrated spin systems on Kagome lattices have long been considered to be apromising candidate for realizing exotic spin liquid phases. Recently, therehas been a lot of renewed interest in these systems with the discovery ofmaterials such as Volborthite and Herbertsmithite that have Kagome likestructures. In the presence of an external magnetic field, these frustratedsystems can give rise to magnetization plateaus of which the plateau at$m=\frac{1}{3}$ is considered to be the most prominent. Here we study theproblem of the antiferromagnetic spin-1/2 quantum XXZ Heisenberg model on aKagome lattice by using a Jordan-Wigner transformation that maps the spins ontoa problem of fermions coupled to a Chern-Simons gauge field. This mappingrelies on being able to define a consistent Chern-Simons term on the lattice.Using a recently developed method to rigorously extend the Chern-Simons term tothe frustrated Kagome lattice we can now formalize the Jordan-Wignertransformation on the Kagome lattice. We then discuss the possible phases thatcan arise at the mean-field level from this mapping and focus specifically onthe case of $\frac{1}{3}$-filling ($m=\frac{1}{3}$ plateau) and analyze theeffects of fluctuations in our theory. We show that in the regime of $XY$anisotropy the ground state at the $1/3$ plateau is equivalent to a bosonicfractional quantum Hall Laughlin state with filling fraction $1/2$ and that atthe $5/9$ plateau it is equivalent to the first bosonic Jain daughter state atfilling fraction $2/3$.

Chern-Simons theory of the magnetization plateaus of the spin-1/2 quantum XXZ Heisenberg model on Kagome Lattice