Harvard Condensed Matter Theory Seminars
The FQHE at half-filled second Landau level (5/2 and 7/2)
has been a long standing enigma. The popular Pfaffian model
of Moore and Read, applied to the 5/2 FQHE by Greiter, Wen,
and Wilczek, is reviewed and scrutinized.
In a exact diagonalization study on finite systems I show
that the Pfaffian model provides an inaccurate description
of the excitations, whose non-Abelian braiding statistics has
been exploited in several quantum computing hardware proposals.
I present an alternative understanding of the 5/2 FQHE within
the composite fermion theory without the Pfaffian.
I argue that the residual interaction between composite
fermions plays a crucial role in establishing incompressibility
at 5/2. The low-energy spectrum and the activation gap are
estimated with the help of a pertubative procedure that
incorporates inter-composite-fermion interactions. This approach
is amenable to systematic perturbative improvements, and produces
ground as well as excited states. It, however, does not relate
to non-Abelian statistics in any obvious manner.
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