Abstract
Recently it was shown that anyons on the two-sphere naturally arise from a system of molecular impurities exchanging angular momentum with a many-particle bath (Phys. Rev. Lett. 126, 015301 (2021)). Here we further advance this approach and rigorously demonstrate that in the experimentally realized regime the lowest spectrum of two linear molecules immersed in superfluid helium corresponds to the spectrum of two anyons on the sphere. We develop the formalism within the framework of the recently experimentally observed angulon quasiparticle.
Highlights
The discovery of the fractional Quantum Hall Effect and the advent and application of topological quantum field theories have revolutionized our understanding of the quantum properties of matter [1,2,3,4,5,6,7,8]
An anyon is a type of quasiparticle that can arise in systems confined to two dimensions and whose exchange properties interpolate between bosons and fermions [13,14,15]
The analysis of anyons on the sphere becomes much more difficult than the wellstudied planar case, mainly because of non separation of center of mass from relative variables. This problem has been stressed and tackled in recent studies of anyons on the two-sphere [30,31,35], which have been successful in computing the spectrum of two anyons subject to a homogeneous magnetic field
Summary
The discovery of the fractional Quantum Hall Effect and the advent and application of topological quantum field theories have revolutionized our understanding of the quantum properties of matter [1,2,3,4,5,6,7,8]. Because of the topological peculiarities of two spatial dimensions, the world lines of anyons can braid nontrivially around each other [13,16,17], and unlike fermions or bosons, exchanging two anyons twice is not topologically equivalent to leaving them alone This opens up a whole new domain of quantum statistics known as intermediate or fractional statistics. There, it has been shown that the emerging statistical interaction manifests itself in the alignment of molecules, which could be of use as a powerful technique to measure the statistics parameter This paves the way towards experimental realization as well as detection of anyons on the sphere using molecular impurities. Note that the phenomenon of quantum statistics transmutation typically involves emergent scalar interaction potentials and non-statistical gauge fields as well, and it is necessary to have sufficient control of these effects in order to provide robust signatures of anyons
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