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(Dublin Institute for Advanced Studies)
Trial wave functions like the famous Laughlin wave function have
played an essential role in the early stages of examination of all
observed conductance plateaus of the fractional quantum Hall effect.
After a short introduction to the general principles involved in
constructing such wave functions I will focus on a particular
hierarchy of trial wave functions which may explain most of the
observed conductance plateaus in the second Landau level. These wave
functions can be viewed as descendants of the quantum Hall state at
filling fraction 5/2, which has recently come under close experimental
investigation, because it is expected to allow for quasiparticle
excitations with exchange behaviour described by a non-Abelian
representation of the braid group (non-Abelian anyons). The newly
proposed hierarchy inherits this feature. Experimental and numerical
signatures of the new states will be discussed and compared to those
of competing states. I will also include some comments on the possible
consequences for topologically fault tolerant quantum computation
based on fractional quantum Hall anyons.