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

We study the persistent current of correlated spinless electrons in acontinuous one-dimensional ring with a single weak link. We includecorrelations by solving the many-body Schrodinger equation for several tens ofelectrons interacting via the short-ranged pair interaction V(x - x'). We solvethis many-body problem by advanced configuration-interaction (CI) and diffusionMonte Carlo (DMC) methods. Our CI and DMC results show, that the persistentcurrent (I) as a function of the ring length (L) exhibits for large L the powerlaw typical of the Luttinger liquid, $I \propto L^{-1-\alpha}$, where the power$\alpha$ depends only on the electron-electron (e-e) interaction. For stronge-e interaction the previous theories predicted for $\alpha$ the formula$\alpha = {(1 + 2 \alpha_{RG})}^{1/2} - 1$, where $\alpha_{RG} =[V(0)-V(2k_F)]/2\pi \hbar v_F$ is the renormalisation-group result for weaklyinteracting electrons, with V(q) being the Fourier transform of V(x-x'). Ournumerical data show that this theoretical result holds in the continuous modelonly if the range of V(x - x') is small (roughly $d \lesssim 1/2k_F$, moreprecisely $4d^2k_F^2 << 1$). For strong e-e interaction ($\alpha_{RG} > 0.25$)our CI data show the power law $I \propto L^{-1-\alpha}$ already for rings withonly ten electrons, i.e., ten electrons are already enough to behave like theLuttinger liquid. The DMC data for $\alpha_{RG} > 0.25$ are damaged by theso-called fixed-phase approximation. Finally, we also treat the e-e interactionin the Hartree-Fock approximation. We find the exponentially decaying I(L)instead of the power law, however, the slope of log(I(L)) still depends solelyon the parameter $\alpha_{RG}$ as long as the range of V(x - x') approacheszero.

Persistent current of Luttinger liquid in one-dimensional ring with weak  link: Continuous model studied by configuration interaction and quantum Monte  Carlo