title: Exact parent Hamiltonian for the quantum Hall states in a lattice.
abstract: We study lattice models of charged particles in uniform magnetic fields. We show how longer range hopping can be engineered to produce a massively degenerate manifold of single-particle ground states with wave functions identical to those making up the lowest Landau level of continuum electrons in a magnetic field. We find that in the presence of local interactions, and at the appropriate filling factors, Laughlin's fractional quantum Hall wave function is an exact many-body ground state of our lattice model. The hopping matrix elements in our model fall off as a Gaussian, and when the flux per plaquette is small compared to the fundamental flux quantum one only needs to include nearest and next-nearest neighbor hoppings. We suggest how to realize this model using atoms in optical lattices, and describe observable consequences of the resulting fractional quantum Hall physics.
authors.affiliation: Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York, USA.
authors.forename: Eliot
authors.initials: E
authors.lastname: Kapit
authors.forename: Erich
authors.initials: E
authors.lastname: Mueller