Unraveling the Physics of Quantum Hall Edge States

Abstract

The primary goal of this thesis is to understand the edge states of quantum Hall systems. In the initial part of the thesis, we explore the integer quantum Hall edge states and bosonize them. The fact that IQHE is a non-interacting phenomenon makes it easier to connect the microscopic picture with the effective field theory. After that, we looked at the edge states of fractional quantum Hall system from the framework of Chern-Simons theory. There is also a microscopic understanding of edge excitation in FQHE. Connecting these two descriptions of the edge is challenging. We gained some insight in this direction by studying both pictures. In the final section, we studied the robustness of these edge states using the null vector criterion and an equivalent of the same. Several example systems were explored in order to come up with simple models of quantum Hall edge interfaces that are numerically tractable.