Dipoles at $\nu =1$

TL;DR

This paper investigates bosonic particles at filling factor one in a strong magnetic field, mapping their interactions to a fermionic dipole gas and analyzing its physical properties.

Contribution

It introduces a fermionic dipole model for composite fermions at , providing a new perspective on their interactions and physical behavior.

Findings

Composite fermions behave as a dipole gas.

Interactions are effectively short-range and screened.

The model predicts properties like effective mass and conductivity.

Abstract

We consider the problem of Bosonic particles interacting repulsively in a strong magnetic field at the filling factor $\nu =1.$ We project the system in the Lowest Landau Level and map the dynamics into an interacting Fermion system. We study the resulting Hamiltonian in the Hartree--Fock approximation in the case of a $\delta $ repulsive potential. The physical picture which emerges is in agreement with the proposal of N. Read that the composite Fermions behave as a gas of dipoles. We argue that the consequence of this is that the composite Fermions interact with screened short range interactions. We develop a Landau theory which we also expect to describe the physical $\nu =1/2$ Fermionic state. The Form factor, the effective mass and the conductivity are analised in this model.