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

We investigate the nature of the fractional quantum Hall (FQH) state atfilling factor $\nu=13/5$, and its particle-hole conjugate state at $12/5$,with the Coulomb interaction, and address the issue of possible competingstates. Based on a large-scale density-matrix renormalization group (DMRG)calculation in spherical geometry, we present evidence that the physics of theCoulomb ground state (GS) at $\nu=13/5$ and $12/5$ is captured by the $k=3$parafermion Read-Rezayi RR state, $\text{RR}_3$. We first establish that thestate at $\nu=13/5$ is an incompressible FQH state, with a GS protected by afinite excitation gap, with the shift in accordance with the RR state. Then, byperforming a finite-size scaling analysis of the GS energies for $\nu=12/5$with different shifts, we find that the $\text{RR}_3$ state has the lowestenergy among different competing states in the thermodynamic limit. We find thefingerprint of $\text{RR}_3$ topological order in the FQH $13/5$ and $12/5$states, based on their entanglement spectrum and topological entanglemententropy, both of which strongly support their identification with the$\text{RR}_3$ state. Furthermore, by considering the shift-freeinfinite-cylinder geometry, we expose two topologically-distinct GS sectors,one identity sector and a second one matching the non-Abelian sector of theFibonacci anyonic quasiparticle, which serves as additional evidence for the$\text{RR}_3$ state at $13/5$ and $12/5$.

The Fractional Quantum Hall States at $\nu=13/5$ and $12/5$ and their Non-Abelian Nature