Characterization of topological states on a lattice with Chern number

Mohammad Hafezi, Anders S. Sorensen, Mikhail D. Lukin, Eugene Demler

Published 2007-06-06, updated 2007-12-04Version 2

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 conventional overlap calculation with known continuum case such as 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.