Molecular Impurities as a Realization of Anyons on the Two-Sphere

TL;DR

This paper proposes a new approach to realize and study anyons on the sphere using molecular impurities, highlighting the effects of topology on quantum statistics and providing a potential experimental pathway.

Contribution

It introduces a model connecting molecular impurities to anyonic spectra on the sphere, advancing the experimental and numerical study of anyons in curved geometries.

Findings

Spectrum of two anyons on the sphere with a Dirac monopole field calculated

Lowest-energy spectrum of molecules matches anyonic spectrum on the sphere

New method to measure the statistics parameter via molecular exchange

Abstract

Studies on experimental realization of two-dimensional anyons in terms of quasiparticles have been restricted, so far, to only anyons on the plane. It is known, however, that the geometry and topology of space can have significant effects on quantum statistics for particles moving on it. Here, we have undertaken the first step towards realizing the emerging fractional statistics for particles restricted to move on the sphere, instead of on the plane. We show that such a model arises naturally in the context of quantum impurity problems. In particular, we demonstrate a setup in which the lowest-energy spectrum of two linear bosonic/fermionic molecules immersed in a quantum many-particle environment can coincide with the anyonic spectrum on the sphere. This paves the way towards experimental realization of anyons on the sphere using molecular impurities. Furthermore, since a change in the alignment of the molecules corresponds to the exchange of the particles on the sphere, such a realization reveals a novel type of exclusion principle for molecular impurities, which could also be of use as a powerful technique to measure the statistics parameter. Finally, our approach opens up a new numerical route to investigate the spectra of many anyons on the sphere. Accordingly, we present the spectrum of two anyons on the sphere in the presence of a Dirac monopole field.