JCMS: Towards density functional theories for anyons

by Douglas Lundholm (Uppsala University)

Monday 13 May 2024, 10:30 → 12:00 Europe/Stockholm

Albano 3: 6228 - Mega (22 seats) (Albano Building 3)

The precise connection between exchange statistics and exclusion statistics for 2D anyons, i.e. quantum quasiparticles with statistics defined by the braid group, has remained elusive for many years. Only for very small systems have exact analytic or numerical methods been applicable to study the spectrum and ground states. However, during the past decade, progress in the mathematics of quantum mechanics has led to rigorous derivations of density functional theories for the abelian anyon gas in weakly interacting regimes, close to bosons and fermions, as well as conjectures for stronger intermediate statistics and other interactions. In particular, I plan to discuss a recent result concerning an almost-bosonic Hartree-Chern-Simons model for which we obtain the critical attraction strength for stability, as well as a scale of nonlinear, self-generated Landau levels with quantized vorticity. The latter were first conjectured by Jackiw and Pi in the early 90's. This is joint work with Alireza Ataei and Dinh-Thi Nguyen at Uppsala University.