Nonperturbative emergence of Dirac fermion in strongly correlated composite fermions of fractional quantum Hall effects

TL;DR

This paper introduces a nonperturbative Dirac fermion theory for composite fermions in fractional quantum Hall effects, resolving longstanding symmetry issues and demonstrating stability for key sequences.

Contribution

It develops a nonperturbative Dirac fermion framework that overcomes weaknesses of traditional composite fermion theory and clarifies particle-hole symmetry.

Findings

Dirac fermion emerges nonperturbatively in composite fermion theory

Particle-hole symmetry is resolved by Dirac equation

The theory is stable for main Jain sequences

Abstract

The classic composite fermion field theory (Ref. 1) builds up an excellent framework to uniformly study important physical objects and globally explain anomalous experimental phenomena in fractional quantum Hall physics while there are also inherent weaknesses. We present a nonperturbative emergent Dirac fermion theory from this strongly correlated composite fermion field theory, which overcomes these serious long-standing shortcomings. The particle-hole symmetry of Dirac equation resolves this particle-hole symmetry enigma in the composite fermion field theory. With the help of presented numerical data, we show that for main Jain's sequences of fractional quantum Hall effects, this emergent Dirac fermion theory is most likely nonperturbatively stable.