Fine Structure and Fractional Aharonov-Bohm Effect

TL;DR

This paper reveals a fine structure in the Aharonov-Bohm effect, showing fractional oscillations caused by electron interactions in a Hubbard ring, valid across various densities and interaction strengths.

Contribution

It demonstrates the existence of fractional periodic oscillations in the Aharonov-Bohm effect due to electron-electron and Zeeman interactions, extending understanding of quantum interference in correlated systems.

Findings

Identification of fractional oscillations with periods 1/N and M/N

Coexistence of conventional and fractional oscillations at low density

Validity of results for arbitrary Hubbard U values

Abstract

We find a fine structure in the Aharonov-Bohm effect, characterized by the appearence of a new type of periodic oscillations having smaller fractional period and an amplitude, which may compare with the amplitude of the conventional Aharonov-Bohm effect. Specifically, at low density or strong coupling on a Hubbard ring can coexist along with the conventional Aaronov-Bohm oscillations with the period equal to an integer, measured in units of the elementary flux quantum, two additional oscillations with periods $1/N$ and $M/N$. The integers $N$ and $M$ are the particles number and the number of down-spin particles, respectively. {}From a solution of the Bethe ansatz equations for $N$ electrons located on a ring in a magnetic field we show that the fine structure is due to electron-electron and Zeeman interactions. Our results are valid in the dilute density limit and for an arbitrary value of the Hubbard repulsion $U$