Speaker
Ask Ellingsen & Filippa Getzner, Uppsala University
Abstract
We study a Chern-Simons-Schrödinger (CSS) energy functional, which has been proposed as an effective mean-field theory for a gas of abelian anyons. For certain critical values of the model parameters, one finds explicit manifolds of ground states, dubbed non-linear Landau levels (NLL) by analogy with the 2D electron gas (2DEG). In the 2DEG, Laughlin and others predicted the emergence of anyonic quasiparticles using a trial state in the lowest Landau level. In this theory, we may expect to see the emergence of quasiparticles behaving as non-abelian anyons, using trial states from the NLL:s.
We will discuss two results in this direction. First, we investigate the usefulness of NLL states as approximate minimisers when the model parameters are moved away from criticality. This is done by explicitly calculating their energies and comparing them to numerical approximations of the true ground state energy. Second, we study the geometry of the NLL manifolds via the associated Berry’s phase and outline the role it plays in shaping the statistics of the emergent quasiparticles.
This talk is based on joint work with Douglas Lundholm and Alireza Ataei.