Fractional Quantum Hall Effect of Lattice Bosons Near Commensurate Flux

Abstract

We study interacting bosons on a lattice in a magnetic field. When the number of flux quanta per plaquette is close to a rational fraction, the low energy physics is mapped to a multi-species continuum model: bosons in the lowest Landau level where each boson is given an internal degree of freedom, or pseudospin. We find that the interaction potential between the bosons involves terms that do not conserve pseudospin, corresponding to umklapp processes, which in some cases can also be seen as BCS-type pairing terms. We argue that in experimentally realistic regimes for bosonic atoms in optical lattices with synthetic magnetic fields, these terms are crucial for determining the nature of allowed ground states. In particular, we show numerically that certain paired wavefunctions related to the Moore-Read Pfaffian state are stabilized by these terms, whereas certain other wavefunctions can be destabilized when umklapp processes become strong.

5 pages, 1 figure

References in corpus (12)

• Non-Abelian Anyons and Topological Quantum Computation
• High temperature fractional quantum Hall states
• Fractional quantum Hall states at zero magnetic field
• Nearly-flat bands with nontrivial topology
• Fractional Quantum Hall Effect in Optical Lattices
• Optical Flux Lattices for Ultracold Atomic Gases
• Composite Fermion Theory for Bosonic Atoms in Optical Lattices
• Paired composite fermion wavefunctions
• Optical lattice quantum Hall effect
• Condensed Groundstates of Frustrated Bose-Hubbard Models
• Bogoliubov theory of interacting bosons on a lattice in a synthetic magnetic field
• Gaussian potentials facilitate access to quantum Hall states in rotating Bose gases

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