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

Abstract

We consider trial wave functions exhibiting $\text{SU}(K)$ 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 $\text{SU}(K)$ 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.