Monte Carlo approach to phase transitions in quantum systems

We propose algorithms of the path-ingetral-based quantum Monte Carlo simulation, which is otherwise prohibitively slow. While the basic idea is the loop-cluster update, there are some important "tricks" that are vital to make the simulation practical. In the present paper, we show two such techniques and their successful applications to the two-dimensional SU(N) Heisenberg model and the three-dimensional Bose Hubbard model. In the former, we obtain a new type of the valence-bond-solid state for the two-boson representation, while in the latter we equillibrate a system of which the size is comparable to a typical experiment of optical lattices.