Real space renormalization of the Mott-insulator to Bose-glass transition in the disordered Bose-Hubbard model

We show the explicit breakdown of self-averaging, due to rare region Griffiths physics, in the disordered Bose-Hubbard model . The real space renormalization flow of the disorder is toward a Gaussian distribution with vanishing relative variance in the Mott insulator, whereas the Bose glass distribution becomes distinctly non-Gaussian with diverging relative variance. We explore distributions which correspond to a non-trivial fixed point in the renormalization group equations.