Quantum Hall Physics - hierarchies and CFT techniques

TL;DR

This paper reviews the development of fractional quantum Hall effect theories, emphasizing hierarchies, conformal field theory techniques, and recent advances in understanding complex quantum Hall states.

Contribution

It provides a comprehensive overview of the evolution and current state of quantum Hall physics, highlighting new theoretical approaches and recent progress.

Findings

Hierarchies of quasiparticles explain fractional quantum Hall states

Conformal field theory techniques have advanced understanding of topological phases

Recent developments include nonabelian quantum Hall liquids

Abstract

The fractional quantum Hall effect, being one of the most studied phenomena in condensed matter physics during the past thirty years, has generated many groundbreaking new ideas and concepts. Very early on it was realized that the zoo of emerging states of matter would need to be understood in a systematic manner. The first attempts to do this, by Haldane and Halperin, set an agenda for further work which has continued to this day. Since that time the idea of hierarchies of quasiparticles condensing to form new states has been a pillar of our understanding of fractional quantum Hall physics. In the thirty years that have passed since then, a number of new directions of thought have advanced our understanding of fractional quantum Hall states, and have extended it in new and unexpected ways. Among these directions is the extensive use of topological quantum field theories and conformal field theories, the application of the ideas of composite bosons and fermions, and the study of nonabelian quantum Hall liquids. This article aims to present a comprehensive overview of this field, including the most recent developments.