Quantum Hall Circle

Abstract

We consider spin-polarized electrons in a single Landau level on a cylinder as the circumference of the cylinder goes to infinity. This gives a model of interacting electrons on a circle where the momenta of the particles are restricted and there is no kinetic energy. Quantum Hall states are exact ground states for appropriate short range interactions, and there is a gap to excitations. These states develop adiabatically from this one-dimensional quantum Hall circle to the bulk quantum Hall states and further on into the Tao-Thouless states as the circumference goes to zero. For low filling fractions a gapless state is formed which we suggest is connected to the Wigner crystal expected in the bulk.

12 pages, published

References in corpus (6)

• Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
• Incompressible Quantum Liquids and New Conservation Laws
• Quantum Hall system in Tao-Thouless limit
• Laughlin State on Stretched and Squeezed Cylinders and Edge Excitations in Quantum Hall Effect
• Half-Filled Lowest Landau Level on a Thin Torus
• Microscopic theory of the quantum Hall hierarchy

Cited by in corpus (7)

• Entanglement Scaling of Fractional Quantum Hall states through Geometric Deformations
• Effective spin chains for fractional quantum Hall states
• Link between the hierarchy of fractional quantum Hall states and Haldane's conjecture for quantum spin chains
• Beyond the Tao-Thouless limit of the fractional quantum Hall effect: spin chains and Fermi surface deformation
• A novel class of translationally invariant spin chains with long-range interactions
• Adiabatic preparation of fractional Chern insulators from an effective thin-torus limit
• Vortex and fractional quantum Hall phases in a rotating anisotropic Bose gas