Fractional Quantum Hall Effect and Featureless Mott Insulators

Abstract

We point out and explicitly demonstrate a close connection that exists between featureless Mott insulators and fractional quantum Hall liquids. Using magnetic Wannier states as the single-particle basis in the lowest Landau level (LLL), we demonstrate that the Hamiltonian of interacting bosons in the LLL maps onto a Hamiltonian of a featureless Mott insulator on triangular lattice, formed by the magnetic Wannier states. The Hamiltonian is remarkably simple and consists only of short-range repulsion and ring-exchange terms.

7 pages, 1 figure. Published version.

References in corpus (6)

• Supersolid hardcore bosons on the triangular lattice
• An exact chiral spin liquid with non-Abelian anyons
• Spin Hamiltonian for which the Chiral Spin Liquid is the Exact Ground State
• Quantum Hall system in Tao-Thouless limit
• Fractionalization, topological order, and quasiparticle statistics
• Strong-Coupling Phases of Frustrated Bosons on a 2-leg Ladder with Ring Exchange

Cited by in corpus (11)

• Interaction effects and quantum phase transitions in topological insulators
• Kaleidoscope of exotic quantum phases in a frustrated XY model
• Fermionization Transform for Certain Higher-Dimensional Quantum Spin Models
• Mott transition for a Lieb-Liniger gas in a shallow quasiperiodic potential: Delocalization induced by disorder
• Quantum Fluctuations of Vortex Lattices in Ultracold Gases
• Collective modes of vortex lattices in two-component Bose-Einstein condensates under synthetic gauge fields
• Continuous thermal melting of a two-dimensional Abrikosov vortex solid
• XY ring exchange model with frustrated Ising coupling on the triangular lattice
• Chiral spin liquid from magnetic Wannier states
• The Bose-Hubbard model on a triangular lattice with diamond ring-exchange
• Vortex lattices in binary Bose-Einstein condensates: Collective modes, quantum fluctuations, and intercomponent entanglement