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

## TL;DR

This paper introduces a Chern-Simons field theory-based method to derive model interactions for Pfaffian paired states, including the Moore-Read and PH Pfaffian states, with explicit calculations for Landau level pseudo-potentials.

## Contribution

It presents a novel, simplified approach to derive model interactions for Pfaffian states using Chern-Simons theory, extending to PH Pfaffian states and multi-Landau level correlations.

## Key findings

- Derived model interactions for Moore-Read state
- Formulated general interactions for PH Pfaffian
- Calculated three-body pseudo-potentials for two Landau levels

## Abstract

On the basis of Chern-Simons field-theoretical description we propose a simple method for derivation of model interactions for Pfaffian paired states. We verify the method in the case of Pfaffian (i.e. Moore - Read) state, and derive a general form of the model interaction in the case of 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 pseudo-potentials for two Landau levels.