Bosonic quantum Hall states in single-layer two-dimensional optical lattices

Quantum Hall (QH) states of two-dimensional (2D) single-layer optical lattices are examined using the BoseHubbard model (BHM) in the presence of an artificial gauge field. We study the QH states of both the homogeneous and inhomogeneous systems. For the homogeneous case, we use cluster Gutzwiller mean-field (CGMF) theory with cluster sizes ranging from 2 x 2 to 5 x 5. We then consider the inhomogeneous case, which is relevant to experimental realization. In this case, we use CGMF and exact diagonalization (ED). The ED studies are using lattice sizes ranging from 3 x 3 to 4 x 12. Our results show that the geometries of the QH states are sensitive to the magnetic flux alpha and cluster sizes. For homogeneous systems, among various combinations of 1/5 <= alpha <= 1/2 and filling factor nu, only the QH state of alpha = 1/4 with nu = 1/2, 1, 3/2, and 2 occur as ground states. For other combinations, the competing superfluid (SF) state is the ground state and QH state is metastable. For BHM with envelope potential, all the QH states observed in homogeneous systems exist for box potentials, but none exist for the harmonic potential. The QH states also persist for very shallow Gaussian envelope potential. As a possible experimental signature, we study the two-point correlations of the QH and SF states.