Laughlin states and their quasi-particle excitations on the torus

Abstract

We provide a full derivation of Laughlin's Jastrow-type wave functions for quantized Hall states subject to periodic boundary conditions using an operator formalism. The construction includes the quasi-hole and the technically more challenging quasi-electron excitation, which was left as an open problem in the classic paper by Haldane and Rezayi [Phys. Rev. B 31, 2529 (1985)].

11 pages, no figures

References in corpus (9)

• Non-Abelian Anyons and Topological Quantum Computation
• Anyons and the quantum Hall effect - a pedagogical review
• Spin Hamiltonian for which the Chiral Spin Liquid is the Exact Ground State
• Clustering Properties and Model Wavefunctions for Non-Abelian Fractional Quantum Hall Quasielectrons
• Microscopic theory of the quantum Hall hierarchy
• Landau Level Quantization on the Sphere
• Statistical Phases and Momentum Spacings for One-Dimensional Anyons
• Hall Viscosity of Hierarchical Quantum Hall States
• Quantum Hall wave functions on the torus

Cited by in corpus (10)

• Geometric construction of Quantum Hall clustering Hamiltonians
• Composite Fermions on a Torus
• Fractional quantum Hall effect with unconventional pairing in monolayer graphene
• Quasielectrons as inverse quasiholes in lattice fractional quantum Hall models
• Berry phase of the composite-fermion Fermi Sea: Effect of Landau-level mixing
• Origin of the $\nu =1/2$ fractional quantum Hall effect in wide quantum wells
• Quasielectrons in lattice Moore-Read models
• On the modular covariance properties of composite fermions on the torus
• Continuum limit of lattice quasielectron wavefunctions
• Anisotropy and quench dynamics of quasiholes in fractional quantum Hall liquids