Exact duality and dual Monte Carlo simulation for the bosonic Hubbard model

We derive the exact dual to the bosonic Hubbard model. The dual variables t ake the form of conserved current loops (local and global). Previously this has been done only for the very soft core model at very high density. No s uch approximations are made here. In particular, the dual of the hard core model is shown to have a very simple form, which is then used to construct an efficient Monte Carlo algorithm which is quite similar to the World Line algorithm but with some important differences. For example, with this algo rithm we can measure easily the correlation function of the order parameter (Green function), a quantity which is extremely difficult to measure with the standard World Line algorithm. We demonstrate the algorithm for the one and two dimensional hardcore bosonic Hubbard models. We present results es pecially for the Green function and zero-mode filling fraction in the two d imensional hardcore model.