Supersymmetric Hamiltonian approach to edge excitations in image fractional quantum Hall effect Original Research Article

A supersymmetric Hamiltonian is constructed for the edge excitations of the Moore–Read (Pfaffian) like state, which is a realization of the image supersymmetric CS model. Fermionic generators and their conjugates are introduced to deal with the fermion pairing, whose condensation form a BCS like state. After Bogoliubov transformation, an image supersymmetric and nonrelativistic Hamiltonian is found to take a known form, which is integrable. The main difference between the Moore–Read state and our BCS like state is that the number of fermion pairs in our formalism is not fixed. However, we have also found that the excited states in our model looks similar but not exactly the same as Moore and Readʹs.