Circulating current in 1D Hubbard rings with long-range hopping: Comparison between exact diagonalization method and mean-field approach

TL;DR

This paper compares exact diagonalization and mean-field methods to analyze persistent current in disordered 1D Hubbard rings with long-range hopping, revealing correlation-enhanced currents and flux periodicities.

Contribution

It provides a detailed comparison of two computational approaches for studying persistent currents in complex 1D systems with long-range hopping and disorder.

Findings

Electronic correlation enhances current in disordered rings.

Higher order hopping significantly affects current magnitude.

Half-flux quantum periodic current observed at certain fillings.

Abstract

The interplay between Hubbard interaction, long-range hopping and disorder on persistent current in a mesoscopic one-dimensional conducting ring threaded by a magnetic flux $\phi$ is analyzed in detail. Two different methods, exact numerical diagonalization and Hartree-Fock mean field theory, are used to obtain numerical results from the many-body Hamiltonian. The current in a disordered ring gets enhanced as a result of electronic correlation and it becomes more significant when contributions from higher order hoppings, even if they are too small compared to nearest-neighbor hopping, are taken into account. Certainly this can be an interesting observation in the era of long-standing controversy between theoretical and experimental results of persistent current amplitudes. Along with these we also find half-flux quantum periodic current for some typical electron fillings and kink-like structures at different magnetic fluxes apart from $\phi=0$ and $\pm \phi_0/2$. The scaling behavior of current is also discussed for the sake of completeness of our present analysis.