CMT Seminar: The fractional quantum Hall effect at filling 5/2: are non-abelians real?
One of the most important discoveries in physics in the past 25 years is the fractional quantum Hall effect (FQHE): a many-body strongly interacting system exhibiting the emergence of topological quasiparticles with fractional charged excitations and statistics and, perhaps, even non-Abelian quasiparticles for the FQHE in the second orbital Landau level at even-denominator filling factor 5/2. The 5/2 FQHE is currently motivating scientists partly due to its potential role in topological quantum computation and the fact that it still is mysterious after nearly 20 years. In this talk, I discuss the actual physical reality of the proposed topological non-Abelian Moore-Read Pfaffian description of the 5/2 FQHE. Specifically, theoretically it is found that the quasi-two-dimensional nature of the experimental FQHE systems, i.e., the finite width, produces a physical environment sufficient to stabilize the Moore-Read Pfaffian state (based on exact diagonalization using the spherical and torus geometries). Our results suggest the possibility of creating optimal experimental systems for the 5/2 FQHE state which are more likely to be described by the Pfaffian ansatz. I also mention the possibility of using FQHE bilayer systems to further shed light on the physical reality of the Pfaffian and the possibility of a quantum phase transition between abelian and non-abelian phases of matter. I acknowledge support from Microsoft Project Q and this work is done in collaboration with Sankar Das Sarma and Thierry Jolicoeur.
Host: Marcos Rigol