# Special Seminar: Do I really know how to do perturbation theory? -- Revisiting some simple quantum Hall edges --

## Main Content

The quantum Hall effect is the first known example of topologically non-trivial insulating phases whose bulk excitations are gapped but edge/boundary states are gapless. The quantum Hall edges can then be described using chiral Luttinger liquid as the building block. Until recently, it is generally accepted that by doing a perturbative renormalization group analysis, an implication of chiral Luttinger liquid based edge theory is that the current-voltage relation of the (electron) tunneling between a Fermi liquid and the quantum Hall edge exhibits power law behavior with quantized and universal scaling exponent. However, by looking at some simple quantum Hall edges that admit exact solution, one can see that the commonly accepted prescription of perturbation theory of chiral Luttinger liquid theory does not properly work. I will describe a prescription for a perturbation theory that reproduces the results of the exact solutions and discuss its physical implications, including non-universal behavior of the edge tunneling exponent.