Abelian and non-Abelian states in ν = 2 / 3 bilayer fractional quantum Hall systems

Department of Mathematics, University of California, Santa Barbara, California 93106, USA(Dated: February 11, 2015)There are several possible theoretically allowed non-Abelian fractional quantum Hall (FQH) states that couldpotentially be realized in one- and two- component FQH systems at total filling fraction  = n+ 2=3, forinteger n. Some of these states even possess quasiparticles with non-Abelian statistics that are powerful enoughfor universal topological quantum computation, and are thus of particular interest. Here, we initiate a systematicnumerical study, using both exact diagonalization and variational Monte Carlo, to investigate the phase diagramof FQH systems at total filling fraction = n+ 2=3, including in particular the possibility of the non-AbelianZ