Studies on the 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 toward 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 or fermionic molecules immersed in a quantum many-particle environment can coincide with the anyonic spectrum on the sphere. This paves the way toward the 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 simple 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.
Physical Review Letters
We are grateful to A. Ghazaryan for valuable discussions and also thank the anonymous referees for comments. D.L. acknowledges financial support from the G¨oran Gustafsson Foundation (grant no. 1804) and LMU Munich. M.L. gratefully acknowledges financial support by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreements No 801770).
Brooks M, Lemeshko M, Lundholm D, Yakaboylu E. Molecular impurities as a realization of anyons on the two-sphere. Physical Review Letters. 2021;126(1). doi:10.1103/PhysRevLett.126.015301
Brooks, M., Lemeshko, M., Lundholm, D., & Yakaboylu, E. (2021). Molecular impurities as a realization of anyons on the two-sphere. Physical Review Letters. American Physical Society. https://doi.org/10.1103/PhysRevLett.126.015301
Brooks, Morris, Mikhail Lemeshko, D. Lundholm, and Enderalp Yakaboylu. “Molecular Impurities as a Realization of Anyons on the Two-Sphere.” Physical Review Letters. American Physical Society, 2021. https://doi.org/10.1103/PhysRevLett.126.015301.
M. Brooks, M. Lemeshko, D. Lundholm, and E. Yakaboylu, “Molecular impurities as a realization of anyons on the two-sphere,” Physical Review Letters, vol. 126, no. 1. American Physical Society, 2021.
Brooks M, Lemeshko M, Lundholm D, Yakaboylu E. 2021. Molecular impurities as a realization of anyons on the two-sphere. Physical Review Letters. 126(1), 015301.
Brooks, Morris, et al. “Molecular Impurities as a Realization of Anyons on the Two-Sphere.” Physical Review Letters, vol. 126, no. 1, 015301, American Physical Society, 2021, doi:10.1103/PhysRevLett.126.015301.
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