Persistent current of a Hubbard ring threaded with a magnetic flux

Abstract

The persistent current in microscopic and mesoscopic Hubbard rings threaded with magnetic flux is studied as a function of the flux and the Coulomb repulsion parameter U. For microscopic rings having very large U, we find that as the flux is increased by one quantum, a magnon hole traverses the magnon sea, generating a periodicity of 1/${\mathit{N}}_{\mathit{c}}$ in the persistent current, but with no changes in the overall spin magnetization, in contrast to the earlier suggestion of Kusmartsev. For non-half-filled mesoscopic rings, we use methods developed by Woynarovich for the zero-flux case to build a rather complete picture of the variation of persistent current with magnetic flux. We find the periodicity to be a half flux quantum or a whole one, and show how the critical flux values at which the current reverses vary with system parameters. We show how the behavior characteristic of microscopic rings goes over to that of mesoscopic rings as ${\mathit{N}}_{\mathit{c}}$/U increases.