Dirty Hubbard rings: renormalization group and exact diagonalization studies

TL;DR

This paper investigates mesoscopic Hubbard rings with impurities, revealing a peak in charge stiffness as a function of electron interactions through combined RG analysis and exact diagonalization, highlighting the importance of $4k_F$ impurity scattering.

Contribution

The study introduces RG equations including $4k_F$ impurity scattering, successfully reproducing the peak behavior observed in exact diagonalization results.

Findings

Charge stiffness peaks at certain interaction strengths.

RG with $4k_F$ scattering explains the peak behavior.

Exact diagonalization confirms the RG predictions.

Abstract

We studied mesoscopic Hubbard rings with impurities using the renormalization group (RG) technique and the exact diagonalizations. The exact diagonalization calculations showed that the charge stiffness normalized by the value of clean system has a peak as a function of electron-electron interactions. Previous RG analysis has succeeded to show the enhancement of the stiffness at weak interactions, but does not show the peak behavior. We derived RG equations with $4k_F$ impurity scattering term, which was ignored in the previous studies, and reproduced the overall behavior of the exact diagonalization results.