  Synthetic quantum Hall bilayer (SQHB), realized by optically driven monolayer
graphene in the quantum Hall regime, provides a flexible platform for
engineering quantum Hall phases as discussed in [Phys. Rev. Lett. 119, 247403].
The coherent driving which couples two Landau levels mimicks an effective
tunneling between synthetic layers. The tunneling strength, the effective
Zeeman coupling, and two-body interaction matrix elements are tunable by
varying the driving frequency and the driving strength. Using infinite density
matrix renormalization group (iDMRG) techniques combined with exact
diagonalization (ED), we show that the system exhibits a non-abelian bilayer
Fibonacci phase at filling fraction $\nu = 2/3$. Moreover, at integer filling
$\nu = 1$, the SQHB exhibits quantum Hall ferromagnetism. Using Hartree-Fock
theory and exact diagonalization, we show that excitations of the quantum Hall
ferromagnet are topological textures known as skyrmions.
