Persistent current of correlated electrons in mesoscopic ring with impurity

TL;DR

This paper investigates the persistent current in a one-dimensional mesoscopic ring with electron-electron interactions and a scatterer, revealing Luttinger liquid behavior and confirming theoretical predictions through numerical methods.

Contribution

It provides numerical validation of the Luttinger liquid theory for persistent currents in interacting electron systems with impurities using CI and DMC methods.

Findings

Persistent current follows a power-law decay with ring length.

Numerical values of the decay exponent match theoretical predictions.

CI and DMC methods agree closely in results.

Abstract

The persistent current of correlated electrons in a continuous one-dimensional ring with a single scatterer is calculated by solving the many-body Schrodinger equation for several tens of electrons interacting via the electron-electron (e-e) interaction of finite range. The problem is solved by the configuration-interaction (CI) and diffusion Monte Carlo (DMC) methods. The CI and DMC results are in good agreement. In both cases, the persistent current $I$ as a function of the ring length $L$ exhibits the asymptotic dependence $I \propto L^{-1-\alpha}$ typical of the Luttinger liquid, where the power $\alpha$ depends only on the e-e interaction. The numerical values of $\alpha$ agree with the known formula of the renormalisation-group theory.