Supersymmetric Hamiltonian Approach to Edge Excitations in $\nu = 5/2$ Fractional Quantum Hall Effect

TL;DR

This paper develops a supersymmetric Hamiltonian model for edge excitations in the $ u=5/2$ fractional quantum Hall state, revealing a new integrable structure with BCS-like fermion pairing and differences from the Moore-Read state.

Contribution

It introduces a supersymmetric Hamiltonian framework for edge states in the Moore-Read-like phase, incorporating fermion pairing and non-fixed fermion pairs, extending previous models.

Findings

Hamiltonian is integrable after transformation.

Fermion pairing resembles BCS state.

Excited states differ from Moore-Read predictions.

Abstract

A supersymmetric Hamiltonian is constructed for the edge excitations of the Moore-Read (Pfaffian) like state, which is a realization of the N=2 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, a N=2 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 Read's.