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

Ultra cold polar bosons in a disordered lattice potential, described by the extended Bose-Hubbard model, 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, e.g. 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.

Equilibration of quantum gases

Finding equilibration times is a major unsolved problem in physics with few analytical results. Here we look at equilibration times for quantum gases of bosons and fermions in the regime of negligibly weak interactions, a setting which not only includes paradigmatic systems such as gases confined to boxes, but also Luttinger liquids and the free superfluid Hubbard model. To do this, we focus on two classes of measurements: (i) coarse-grained observables, such as the number of particles in a region of space, and (ii) few-mode measurements, such as phase correlators.Weshow that, in this setting, equilibration occurs quite generally despite the fact that the particles are not interacting. Furthermore, for coarse-grained measurements the timescale is generally at most polynomial in the number of particles N, which is much faster than previous general upper bounds, which were exponential in N. For local measurements on lattice systems, the timescale is typically linear in the number of lattice sites. In fact, for one-dimensional lattices, the scaling is generally linear in the length of the lattice, which is optimal. Additionally, we look at a few specific examples, one of which consists ofNfermions initially confined on one side of a partition in a box. The partition is removed and the fermions equilibrate extremely quickly in time O(1 N).