Dipole representation of half-filled Landau level

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)].

arXiv comment9 pages, 4 figures

References in corpus (10)

• Is the Composite Fermion a Dirac Particle?
• Lowest-Landau-level theory of the quantum Hall effect: the Fermi-liquid-like state
• A dipole interpretation of the $\nu =1/2$ state
• Quantum Boltzmann equation of composite fermions interacting with a gauge field
• Non-commutative field theory and composite Fermi Liquids in some quantum Hall systems
• Pomeranchuk Instability of Composite Fermi Liquids
• Numerical Study of Quantum Hall Bilayers at Total Filling ${\nu }_T=1$: A New Phase at Intermediate Layer Distances
• $s$-wave paired composite-fermion electron-hole trial state for quantum Hall bilayers with $\nu =1$
• Meron deconfinement in the quantum Hall bilayer at intermediate distances
• Microscopic derivation of Dirac composite fermion theory: Aspects of noncommutativity and pairing instabilities

Cited by in corpus (7)

• Zero-field composite Fermi liquid in twisted semiconductor bilayers
• Quantum mechanics of composite fermions
• Quantum Hall bilayer in dipole representation
• On dualities of paired quantum Hall bilayer states at ${\nu }_T=\frac{1}{2}+\frac{1}{2}$
• Topological pairing of composite fermions via criticality
• Exploring the nature of the emergent gauge field in composite-fermion metals: A large-scale microscopic study
• Dipole representation of composite fermions in graphene quantum Hall systems