The persistent current
(I) of the spinless-electron Luttinger liquid is calculated by numerical microscopic methods in the continuous one-dimensional ring containing a weak link with transmission amplitude ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{t}}_{{k}_{F}}⪡1$. The electrons interact via a screened interaction of range
d. If $d\ensuremath{\lesssim}1/2{k}_{F}$, the interaction modifies the transmission as ${t}_{{k}_{F}}\ensuremath{\simeq}{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{t}}_{{k}_{F}}{N}^{\ensuremath{-}\ensuremath{\alpha}}$ and the current as $LI/e{v}_{F}\ensuremath{\simeq}|{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{t}}_{{k}_{F}}|{N}^{\ensuremath{-}\ensuremath{\alpha}}$, where
N is the electron number,
L the ring length,
N/L a fixed density, and $\ensuremath{\alpha}$ depends on the interaction in accord with the renormalization-group (RG) theory. Unlike our results, the RG theory predicts for a finite
d the power laws ${t}_{{k}_{F}}\ensuremath{\simeq}{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{t}}_{{k}_{F}}{(L/d)}^{\ensuremath{-}\ensuremath{\alpha}}$ and $LI/e{v}_{F}\ensuremath{\simeq}|{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{t}}_{{k}_{F}}|{(L/d)}^{\ensuremath{-}\ensuremath{\alpha}}$, both depending on two interaction parameters,
d and $\ensuremath{\alpha}$. To explain why our results depend solely on $\ensuremath{\alpha}$, we show analytically that the interaction-matrix elements depend only on $\ensuremath{\alpha}$ (not on
d) when $d\ensuremath{\lesssim}1/2{k}_{F}$. As
d exceeds
1/2kF, our result for
LI/evF starts to depend on
d as well and likely approaches the result $LI/e{v}_{F}\ensuremath{\simeq}|{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{t}}_{{k}_{F}}|{(L/d)}^{\ensuremath{-}\ensuremath{\alpha}}$ in the limit
L⪢d⪢1/2kF, not feasible by our numerical methods.
We study the persistent current of correlated spinless electrons in a continuous one-dimensional ring with a single weak link. We include correlations by solving the many-body Schrodinger equation for several tens of electrons interacting via the short-ranged pair interaction V(x - x'). We solve this many-body problem by advanced configuration-interaction (CI) and diffusion Monte Carlo (DMC) methods. Our CI and DMC results show, that the persistent current (I) as a function of the ring length (L) exhibits for large L the power law typical of the Luttinger liquid,
I∝L−1−α, where the power
α depends only on the electron-electron (e-e) interaction. For strong e-e interaction the previous theories predicted for
α the formula
α=(1+2αRG)1/2−1, where
αRG=[V(0)−V(2kF)]/2πℏvF is the renormalisation-group result for weakly interacting electrons, with V(q) being the Fourier transform of V(x-x'). Our numerical data show that this theoretical result holds in the continuous model only if the range of V(x - x') is small (roughly
d≲1/2kF, more precisely
4d2kF2<<1). For strong e-e interaction (
αRG>0.25) our CI data show the power law
I∝L−1−α already for rings with only ten electrons, i.e., ten electrons are already enough to behave like the Luttinger liquid. The DMC data for
αRG>0.25 are damaged by the so-called fixed-phase approximation. Finally, we also treat the e-e interaction in 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 solely on the parameter
αRG as long as the range of V(x - x') approaches zero.
Persistent currents–inviscid quantized flow around an atomic circuit–are a crucial building block of atomtronic devices. We investigate how acceleration influences the transfer of persistent currents between two density-connected, ring-shaped atomic Bose-Einstein condensates, joined by a tunable weak link that controls system topology. We find that the acceleration of this system modifies both the density and phase dynamics between the rings, leading to a bias in the periodic vortex oscillations studied in T. Bland et al., Phys. Rev. Research 4, 043171 (2022). Accounting for dissipation suppressing such vortex oscillations, the acceleration facilitates a unilateral vortex transfer to the leading ring. We analyze how this transfer depends on the weak-link amplitude, the initial persistent current configuration, and the acceleration strength and direction. Characterization of the sensitivity to these parameters paves the way for a new platform for acceleration measurements, for which we outline a proof-of-concept ultracold double-ring accelerometer.