The large system asymptotics of persistent currents in mesoscopic quantum rings

TL;DR

This paper investigates the asymptotic behavior of persistent currents in large mesoscopic quantum rings with interactions and impurities, using advanced numerical methods and comparing with analytical solutions.

Contribution

It introduces an improved functional renormalization group approach to analyze persistent currents and validates results with DMRG and exact diagonalization methods.

Findings

Numerical asymptotic power laws for persistent currents up to 32000 sites.

Good agreement between fRG results and Bethe Ansatz predictions.

Extended analysis to low electron densities with DMRG.

Abstract

We consider a one-dimensional mesoscopic quantum ring filled with spinless electrons and threaded by a magnetic flux, which carries a persistent current at zero temperature. The interplay of Coulomb interactions and a single on-site impurity yields a non-trivial dependence of the persistent current on the size of the ring. We determine numerically the asymptotic power law for systems up to 32000 sites for various impurity strengths and compare with predictions from Bethe Ansatz solutions combined with Bosonization. The numerical results are obtained using an improved functional renormalization group (fRG) method. We apply the density matrix renormalization group (DMRG) and exact diagonalization methods to benchmark the fRG calculations. We use DMRG to study the persistent current at low electron concentrations in order to extend the validity of our results to quasi-continuous systems. We briefly comment on the quality of calculated fRG ground state energies by comparison with exact DMRG data.