Simulations of Disordered Bosons on Hyper-Cubic Lattices

We address computational issues relevant to the study of disordered quantum mechanical systems at very low temperatures. As an example we consider the disordered Bose-Hubbard model in three dimensions directly at the Bose-glass to superfluid phase transition. The universal aspects of the critical behaviour are captured by a $(3+1)$ dimensional link-current model for which an efficient ‘worm’ algorithm is known. We present a calculation of the distribution of the superfluid stiffness over the disorder realizations, outline a number of important considerations for performing such estimates, and suggest a modification of the link-current Hamiltonian that improves the numerical efficiency of the averaging procedure without changing the universal properties of the model.