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The Landau level: Half-full or half-empty?
We show here that an extension of the Hamiltonian theory developed by us over
the years furnishes a composite fermion (CF) description of the 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 which has the features
from and implements the the PH transformation on the LLL as
an anti-unitary operator with . 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 . Along the way we also found a representation with all
the features listed above except that now . We suspect it
corresponds to an emergent charge-conjugation symmetry of the boson
problem analyzed by Read.Comment: 10 pages, no figures. Two references and a section on HF adde
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