SU(3) and SU(4) singlet quantum Hall states at $\nu =2\mathrm{/}3$

We report on an exact diagonalization study of fractional quantum Hall states at filling factor $\nu =2\mathrm{/}3$ in a system with a four-fold degenerate $n$=0 Landau level and SU(4) symmetric Coulomb interactions. Our investigation reveals previously unidentified SU(3) and SU(4) singlet ground states which appear at flux quantum shift 2 when a spherical geometry is employed, and lie outside the established composite-fermion or multicomponent Halperin state patterns. We evaluate the two-particle correlation functions of these states, and discuss quantum phase transitions in graphene between singlet states with different number of components as magnetic field strength is increased.