Bosonic Integer and Fractional Quantum Hall effect in an interacting lattice model

We explore the presence of bosonic integer, as well as the fractional quantum Hall effect in an interacting lattice model. Our model is defined over the bipartite honeycomb lattice with $\pi$ magnetic flux per unit cell and is populated by bosons with hardcore constraint. The bosons can hop to the nearest neighbor (simple hopping) and to the next nearest neighbor (correlated hopping). We use the Lanczos algorithm (Exact Diagonalization (ED)) to find the ground state as well as a few excited states of the system with an aim to characterize the different phases of the system. We have performed calculations for two different fillings and provide evidence for the presence of the bosonic integer quantum Hall effect (BIQHE) and the bosonic fractional quantum Hall effect (BFQHE). We also show the phase transition from the bosonic quantum Hall state to the superfluid (SF) state. We have also performed the adiabatic flux threading to confirm the presence of quantum Hall states.