Nonperturbative emergence of the Dirac fermion in a strongly correlated composite Fermi liquid

The classic composite fermion field theory [B. I. Halperin, P. A. Lee, and N. Read, Phys. Rev. B 47, 7312 (1993)] 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 the 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 in mean field approximation is most likely stable.

Figure 1

The energy $E\left(C\right)$ is determined through Eqs. (20) and (22) for the real $C$. The blue (thick) line is for ${\nu }^{*}=1$, the purple (solid) line is for ${\nu }^{*}=2$, and the yellow (dashed) line is for ${\nu }^{*}=3$.