Abelian and Non-Abelian States in $\nu=2/3$ Bilayer Fractional Quantum Hall Systems

Understand

There are several possible theoretically allowed non-Abelian fractional quantum Hall (FQH) states that could potentially be realized in one- and two- component FQH systems at total filling fraction $\nu = n+ 2/3$, for integer $n$.

• Some of these states even possess quasiparticles with non-Abelian statistics that are powerful enough for universal topological quantum computation, and are thus of particular interest.
• Here, we initiate a systematic numerical study, using both exact diagonalization and variational Monte Carlo, to investigate the phase diagram of FQH systems at total filling fraction $\nu = n+2/3$, including in particular the possibility of the non-Abelian $Z_4$ parafermion state.
• In $\nu = 2/3$ bilayers, we determine the phase diagram as a function of interlayer tunneling and repulsion, finding only three competing Abelian states, without the $Z_4$ state.