Mikael Fremling
Laughlin's State and the Plasma Analogy
The Laughlin wave function is the drosophila of representative trial wave functions for the fractional quantum Hall effect, describing e.g. the filling fraction ν=1/3. In this talk I will discuss the connection between Laughlin's wave function and the partition function of a two dimensional one component plasma. I will focus on the properties of this wave function when it has periodic boundary conditions (i.e. is on a torus). On the torus, modular transformations put strong constraints on the analytic structure that the wave functions can have, and also cast light on the type of anyon braiding that is present for the quasi-particles. It also turns out that if one of the torus' perimeters is sufficiently short -- i.e. approaching the thin-torus limit -- the Laughlin plasma fails to screen, which has consequences for the anyonic braiding.