Fractional Chern insulators in coupled chains

The study of fractional quantum Hall states, and in particular their exotic anyonic excitations, poses a major challenge in current research. In particular, cold atoms in optical lattices provide a promising platform to realize and manipulate fractional Chern insulators in the very near future.

Inspired by the success of coupled wire constructions in the continuum, we here discuss a possible route to realization starting from weakly coupled chains in the context of a Hofstadter-Bose-Hubbard model. Performing DMRG calculations, we gain insight into both analytically meaningful quantities (like the central charge or the many-body Chern number) and experimentally accessible observables (like chiral edge currents or on-site correlations). While Luttinger liquid physics dominates in the decoupled limit, close to the isotropic limit we find a topologically non-trivial phase showing signatures of the Laughlin state at filling factor ν = 1/2. This approach is expected to generalize to other filling factors and can be used to develop new adiabatic preparation schemes.