A holesome story: quasiholes and other surprises in the fractional quantum Hall effect
Alexandre Fagerlund
There is a wealth of rich physics associated with the fractional quantum Hall effect. I will give an introduction to some of these ideas, with a focus on the so-called k=3 Read-Rezayi state. The talk will assume only « an epsilon » of prerequisite knowledge, and will gradually introduce some of the basic ideas relevant for the fractional quantum Hall effect. These include some useful wave functions and the notion of quasiholes, which are quasiparticle dips in the electron fluid. I will briefly outline how these concepts can be related to conformal field theory (CFT). The CFT description provides a different perspective on some of the quantum Hall phenomena, and is eventually shown to naturally lead to the language of matrix product states (MPS), which can be used for efficient numerical computations for fractional quantum Hall states.
In the second part of the talk, I will outline some of my own research. This includes a numerical technique developed together with my supervisor, Eddy Ardonne. The technique is based on CFT and MPS, and allows e.g. density profiles and spins of quasiholes in the k=3 Read-Rezayi state to be computed. From these spins, braiding phases of quasiholes can be inferred. Together with Leonardo Mazza and Alberto Nardin, we have also used these methods to numerically demonstrate a form of bulk-boundary correspondence in fractional quantum Hall states, where spin fractionalizes between a quasihole in the bulk and the distorted edge. This topic will be subject to more research during my stay here.