Characterization of topological states on a lattice with Chern numberM. Hafezi1, A. S. Sørensen2, M. D. Lukin1 and E. Demler1
1 Physics Department, Harvard University - Cambridge, MA - 02138, USA
2 QUANTOP, Danish National Research Foundation Centre of Quantum Optics, Niels Bohr Institute DK-2100 Copenhagen Ø, Denmark
received 20 September 2007; accepted in final form 2 November 2007; published January 2008
published online 27 November 2007
We study Chern numbers to characterize the ground state of strongly interacting systems on a lattice. This method allows us to perform a numerical characterization of bosonic fractional quantum Hall (FQH) states on a lattice where the conventional overlap calculation with the known continuum case such as the Laughlin state, breaks down due to the lattice structure or dipole-dipole interaction. The non-vanishing Chern number indicates the existence of a topological order in the degenerate ground-state manifold.
03.75.Lm - Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices, and topological excitations.
73.43.-f - Quantum Hall effects.
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