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

TL;DR

This paper explores SU(K) symmetric trial wavefunctions for the fractional quantum Hall effect, using plasma analogy and exact diagonalization to identify stable states and analyze their properties in systems with internal degrees of freedom.

Contribution

It generalizes Laughlin's plasma analogy to SU(K) systems and establishes stability criteria, reducing candidate wavefunctions for fractional quantum Hall states.

Findings

Identified stable and unstable SU(K) wavefunctions for various systems.

Validated stability criteria with exact diagonalization for SU(2) and SU(4).

Analyzed pair-correlation functions of ground states and excitations.

Abstract

We consider trial wavefunctions 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), semiconductors 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 wavefunctions 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 are 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.