PDEA Seminar: Berry Phases in Nonlinear Landau Levels

Abstract: Anyons are quantum particles that are neither bosons nor fermions. We study an effective model for a 2D gas of anyons, given by a certain energy functional. The manifolds of minimisers of this functional were characterised in recent work by Ataei, Lundholm, and Nguyen, who dubbed them “nonlinear Landau levels” (NLL:s). In this talk, I will present ongoing work towards understanding the geometry of these spaces of minimisers using Berry connections and their holonomies, and discuss how they relate to the quantum statistics of emergent quasiparticles.

This is a seminar in the PDEs and Applications seminar series.