The $\nu =\frac{1}{2}$ Landau level: Half-full or half-empty?

Abstract

We show here that an extension of the Hamiltonian theory developed by us over the years furnishes a composite fermion (CF) description of the $\nu =\frac{1}{2}$ state that is particle-hole (PH) symmetric, has a charge density that obeys the magnetic translation algebra of the lowest Landau level (LLL), and exhibits cherished ideas from highly successful wave functions, such as a neutral quasi-particle with a certain dipole moment related to its momentum. We also a provide an extension away from $\nu =\frac{1}{2}$ which has the features from $\nu =\frac{1}{2}$ and implements the the PH transformation on the LLL as an anti-unitary operator $\mathcal{T}$ with ${\mathcal{T}}^2=-1$. This extension of our past work was inspired by Son, who showed that the CF may be viewed as a Dirac fermion on which the particle-hole transformation of LLL electrons is realized as time-reversal, and Wang and Senthil who provided a very attractive interpretation of the CF as the bound state of a semion and anti-semion of charge $\pm \frac{e}{2}$. Along the way we also found a representation with all the features listed above except that now ${\mathcal{T}}^2=+1$. We suspect it corresponds to an emergent charge-conjugation symmetry of the $\nu =1$ boson problem analyzed by Read.

10 pages, no figures. Two references and a section on HF added

References in corpus (9)

• Particle-hole symmetry and the Pfaffian state
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• Is the Composite Fermion a Dirac Particle?
• Dual Dirac liquid on the surface of the electron topological insulator
• Particle-Hole Symmetry and the Composite Fermi Liquid
• Mirror symmetry and the half-filled Landau level
• Luttinger theorem for the strongly correlated Fermi liquid of composite fermions
• Self Duality and a possible Hall-insulator phase near the superconductor-to-insulator transition in two-dimensional indium-oxide films
• Hamiltonian theory of the half-filled Landau level with disorder: Application to recent NMR data

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