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Motivated by recent experiments on toroidal Bose-Einstein condensates inall-optical traps with tunable weak links, we study the one-dimensionalBose-Hubbard model on a ring-shaped lattice with a small region of weak hoppingintegrals using quantum Monte Carlo simulations. Besides the usual Mottinsulating and superfluid phases, we find a phase which is compressible but nonsuperfluid with a local Mott region. This `local Mott' phase extends in a largeregion of the phase diagram. These results suggest that the insulating andconducting phases can be tuned by a local parameter which may provide a newinsight to the design of atomtronic devices.

Phase diagram of the Bose-Hubbard model on a ring-shaped lattice with tunable weak links