Superfluid to Bose-glass transition of hard core bosons in one-dimensional incommensurate optical lattice

We study superfluid to Anderson insulator transition of strongly repulsive Bose gas in a one dimensional incommensurate optical lattice. In the hard core limit, the Bose-Fermi mapping allows us to deal with the system exactly by using the exact numerical method. Based on the Aubry-Andr\'{e} model, we exploit the phase transition of the hard core boson system from superfluid phase with all the single particle states being extended to the Bose glass phase with all the single particle states being Anderson localized as the strength of the incommensurate potential increasing relative to the amplitude of hopping. We evaluate the superfluid fraction, the one particle density matrices, momentum distributions, the natural orbitals and their occupations. All of these quantities show that there exists a phase transition from superfluid to insulator in the system.