Illustration of spin-half wave-functions, and other fractional-spin structures

TL;DR

This paper illustrates geometric structures exhibiting spin-half wave-function properties, explores fractional-spin structures, and proposes a polymer synthesis as a potential physical realization of a quasi-spin-1/3 system.

Contribution

It introduces the concept of fractional-spin geometric structures and discusses their theoretical and group-theoretical aspects, along with a proposed synthesis for physical realization.

Findings

Demonstration of spin-half wave-function characteristics in geometric structures

Proposal of fractional-spin structures beyond traditional spin-half

Synthesis of a twisted ring polymer as a quasi-spin-1/3 realization

Abstract

We provide an illustration of a geometric structure that exhibits the spin-half wave-function characteristics, namely that its full rotation displays a phase inversion. We show that general fractional-spin geometric structures are possible, along with sketchy discussions concerning group-theoretical and quantum descriptions, as well as pose some queries. Synthesis of a $(PF_3)_n$-chain polymer in the form of a twisted ring is proposed as a realization of a quazi-spin-1/3 structure.