Bosonization and entanglement spectrum for one-dimensional polar bosons on disordered lattices

Understand

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.