Model interactions for Pfaffian paired states based on Chern-Simons field theory description

On the basis of a Chern-Simons field-theoretical description we propose a simple method for the derivation of model interactions for Pfaffian paired states. We verify the method in the case of the Pfaffian (i.e., Moore-Read) state and derive a general form of the model interaction in the case of the particle-hole (PH) Pfaffian. More than one Landau level is needed to establish the correlations of the PH Pfaffian, and we present the values of relevant three-body pseudopotentials for two Landau levels.

Figure 1

Schematic phase diagram as the pairing parameter $\lambda$ is varied.

Figure 2

Matrix elements of three-body pseudopotentials in the lowest Landau level for $\lambda =-1$ (above) and $\lambda =0$ (bottom).

Figure 3

Three-body pseudopotential matrix elements for $\lambda =1$ (PH Pfaffian case) in the second Landau level (top), for states with two particles in the second Landau level and one in the lowest Landau level (middle), and in the lowest Landau level (bottom).