Dipole representation of half-filled Landau level

TL;DR

This paper develops a symmetric dipole representation for composite fermions in a half-filled Landau level, incorporating particle-hole symmetry and matching numerical Fermi liquid parameters.

Contribution

It introduces a novel symmetric dipole representation with a special constraint, improving the theoretical description of composite fermions at half-filling.

Findings

The effective Hamiltonian commutes with the physical constraint.

The model achieves boost invariance on the Fermi level.

Calculated F2 parameter agrees with numerical results.

Abstract

We introduce a variant of dipole representation for composite fermions in a half-filled Landau level, taking into account the symmetry under exchange of particles and holes. This is implemented by a special constraint on composite fermion and composite hole degree of freedom (of an enlarged space), that makes the resulting composite particle, dipole, a symmetric object. We study an effective Hamiltonian, that commutes with the constraint on the physical space, and fulfills the requirement for boost invariance on the Fermi level. The calculated Fermi liquid parameter F2 is in a good agreement with numerical investigations in [Phys. Rev. Lett. 121, 147601 (2018)].