  The extended Bose-Hubbard model subjected to a disordered potential is
predicted to display a rich phase diagram. In the case of uniform random
disorder one finds two insulating quantum phases -- the Mott-insulator and the
Haldane insulator -- in addition to a superfluid and a Bose glass phase. In the
case of a quasiperiodic potential further phases are found, eg the
incommensurate density wave, adiabatically connected to the Haldane insulator.
For the case of weak random disorder we determine the phase boundaries using a
perturbative bosonization approach. We then calculate the entanglement spectrum
for both types of disorder, showing that it provides a good indication of the
various phases.
