Plasma picture of the fractional quantum Hall effect with internal SU(K) symmetries

We consider trial wave functions exhibiting SU(K) symmetry, which may be well suited to grasp the physics of the fractional quantum Hall effect with internal degrees of freedom. Systems of relevance may be either spin-unpolarized states (K=2), semiconductor bilayers (K=2,4), or graphene (K=4). We find that some introduced states are unstable, undergoing phase separation or phase transition. This allows us to strongly reduce the set of candidate wave functions eligible for a particular filling factor. The stability criteria are obtained with the help of Laughlin’s plasma analogy, which we systematically generalize to the multicomponent SU(K) case. The validity of these criteria is corroborated by exact-diagonalization studies for SU(2) and SU(4). Furthermore, we study the pair-correlation functions of the ground state and elementary charged excitations within the multicomponent plasma picture.