Generic incommensurate transition in the two-dimensional boson Hubbard model

The generic transition in the boson Hubbard model, occurring at an incommensurate chemical potential, is studied in the link-current representation using the recently developed directed geometrical worm algorithm. We find clear evidence for a multipeak structure in the energy distribution for finite lattices, usually indicative of a first-order phase transition. However, this multipeak structure is shown to disappear in the thermodynamic limit, revealing that the true phase transition is second order. These findings cast doubts over the conclusion drawn in a number of previous works considering the relevance of disorder at this transition.