Lectures on the Quantum Hall Effect

TL;DR

This paper provides a comprehensive theoretical overview of the quantum Hall effect, covering microscopic wavefunctions, effective field theories, and boundary modes, aimed at graduate students with quantum field theory background.

Contribution

It offers a unified presentation of the quantum Hall effect's theoretical structures, including both integer and fractional phenomena, with emphasis on Chern-Simons theories and edge modes.

Findings

Detailed explanation of Landau levels and Berry phase

Analysis of integer and fractional quantum Hall effects

Discussion of non-Abelian quantum Hall states

Abstract

The purpose of these lectures is to describe the basic theoretical structures underlying the rich and beautiful physics of the quantum Hall effect. The focus is on the interplay between microscopic wavefunctions, long-distance effective Chern-Simons theories, and the modes which live on the boundary. The notes are aimed at graduate students in any discipline where $\hbar=1$. A working knowledge of quantum field theory is assumed. Contents: 1. The Basics (Landau levels and Berry phase). 2. The Integer Quantum Hall Effect. 3. The Fractional Quantum Hall Effect. 4. Non-Abelian Quantum Hall States. 5. Chern-Simons Theories. 6. Edge Modes.