Fractional quantum Hall effect in optical lattices - Gaur, Deepak; Sable, Hrushikesh; Angom, D. (Frontiers in Physics, 2023)
We study the bosonic fractional quantum Hall (FQH) states in a system of ultra-cold bosons in a two-dimensional optical lattice in the presence of a synthetic magnetic field, described by the bosonic Harper-Hofstadter Hamiltonian. We obtain incompressible states as ground states at various filling factors similar to those of the FQH states. We focus in particular on the ν = 1/2 FQH state, and characterize it with the two-point correlation function and many-body Chern number. We further investigate the effect of dipolar interaction on the ν = 1/2 FQH state. We find that dipolar interaction stabilizes the FQH state against the competing superfluid state. We use the cluster Gutzwiller mean-field and exact diagonalization techniques in our work.