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We investigate the ground state properties of a bosonic Harper-Hofstadtermodel with local interactions on a finite cylindrical lattice with fillingfraction $\nu=1/2$. We find that our system supports topologically orderedstates by calculating the topological entanglement entropy, and its value is ingood agreement with the theoretical value for the $\nu=1/2$ Laughlin state. Byexploring the behaviour of the density profiles, edge currents andsingle-particle correlation functions, we find that the ground state on thecylinder shows all signatures of a fractional quantum Hall state even for largevalues of the magnetic flux density. Furthermore, we determine the dependenceof the correlation functions and edge currents on the interaction strength. Wefind that depending on the magnetic flux density, the transition towardsLaughlin-like behaviour can be either smooth or happens abruptly for somecritical interaction strength.

Bosonic Fractional Quantum Hall States on a Finite Cylinder