Thirty Years of Composite Fermions and Beyond

TL;DR

This chapter reviews three recent research directions in composite fermions, including theoretical predictions, density functional theory, and parton theory applications, advancing understanding of fractional quantum Hall phenomena.

Contribution

It provides a comprehensive overview of recent developments in composite fermion research, including new theoretical models and applications to complex quantum Hall states.

Findings

Quantitative predictions for spin polarization transitions

Phase diagram of the crystal

Applications of parton theory to delicate states

Abstract

This chapter appears in "Fractional Quantum Hall Effects: New Development," edited by B. I. Halperin and J. K. Jain (World Scientific, 2020). The chapter begins with a primer on composite fermions, and then reviews three directions that have recently been pursued. It reports on theoretical calculations making detailed quantitative predictions for two sets of phenomena, namely spin polarization transitions and the phase diagram of the crystal. This is followed by the Kohn-Sham density functional theory of the fractional quantum Hall effect. The chapter concludes with recent applications of the parton theory of the fractional quantum Hall effect to certain delicate states.