Seminar: Mathematical physics of the 2D anyon gas

Abstract: I aim to give an overview of a number of results on the many-body quantum mechanics of anyons, i.e. effective quasi-particles that may emerge in two-dimensional geometries subject to a breaking of orientation symmetry. Their logical possibility as quantum statistics intermediate to bosons and fermions has been known since the late 70's and early 80's, but only in the recent years has sufficiently convincing evidence from experiments emerged. The main obstacle to a fundamental understanding of the mathematics and physics of anyon gases is their complex topological interaction. Together with research groups in Denmark, France, Italy, Austria and Switzerland, we have focused mainly on the exchange vs. exclusion statistics of the ideal abelian and the non-abelian anyon gas [1], the extended anyon gas close to bosons or fermions and its density functional theory [2], as well as the emergence of anyons in the fractional quantum Hall context [3] and in systems of polarons [4] and angulons [5].

References:

[1] D. Lundholm, Many-anyon trial states, Phys. Rev. A 96, 012116 (2017); Lundholm and Qvarfordt, Exchange and exclusion in the non-abelian anyon gas, arXiv:2009.12709 (2020)

[2] Correggi et al., Vortex patterns in the almost-bosonic anyon gas, EPL 126, 20005 (2019)

[3] Lundholm and Rougerie, Emergence of fractional statistics for tracer particles in a Laughlin liquid, Phys. Rev. Lett. 116, 170401 (2016); Lambert, Lundholm, Rougerie, Quantum statistics transmutation via magnetic flux attachment, arXiv:2201.03518 (2022)

[4] Yakaboylu et al., A Quantum Impurity Model for Anyons, Phys. Rev. B 102, 144109 (2020)

[5] Brooks et al., Molecular Impurities as a Realization of Anyons on the Two-Sphere, Phys. Rev. Lett. 126, 015301 (2021)