Fractional flux periodicity in tori made of square lattice

TL;DR

This study investigates how the ground state energy and persistent currents in square lattice tori exhibit fractional flux periodicity depending on the twist, revealing new quantum effects in topologically nontrivial systems.

Contribution

It introduces the concept of fractional flux periodicity in square lattice tori and explores its dependence on twist and topology, extending understanding of quantum phenomena in such systems.

Findings

Ground state energy shows fractional flux periodicity.

Persistent currents depend on the twist of the torus.

Fractional periodicity relates to the torus's topology and geometry.

Abstract

This paper describes a study on fractional flux periodicity of the ground state in planar systems made from a square lattice whose boundary is compacted into a torus. It is pointed out that, in the long length and large diameter limit of a torus, the ground-state energy and persistent currents show a fractional period of the fundamental unit of magnetic flux depending on the twist around the torus axis. We discuss the possible relationship between the twist and genus of a torus, and comment on fractional flux periodicity in a cylinder.