PDEA Seminar: Exchange and exclusion in the non-abelian anyon gas

Abstract: Anyons are effective quantum particles that emerge in certain planar systems and have properties intermediate to bosons and fermions. Roughly speaking, they can be defined by extending the Schrödinger wave function to be multivalued, and representing a continuous exchange of coordinates by an arbitrary complex phase (abelian anyons) or, more generally, a unitary matrix (non-abelian anyons). This yields a probabilistic realization of the braid group, with links to knot invariants, conformal field theory, and Chern-Simons theory. Furthermore, anyons have been proposed as potential building blocks for topologically protected quantum computing.

A fundamental mathematical problem concerns the relationship between exchange phases and exclusion (compare Pauli's exclusion principle for fermions). I will discuss how to extend robust analytical methods for exchange and local exclusion (Poincaré, Hardy and Lieb-Thirring inequalities) from fermions to non-abelian anyons, focusing on two of the most popular such models: the Fibonacci and the Ising anyon models.

Reference: Lundholm, Qvarfordt, http://arxiv.org/abs/2009.12709

Participate on site or via Zoom link, meeting ID: 67226102216

This is a seminar in the PDEs and Applications seminar series