Giovanna Morigi
We analyse the quantum phases of the extended Bose-Hubbard model with global interactions. This model describes ultracold bosonic atoms confined by a two-dimensional optical lattice and interacting via global forces mediated by cavity photons. The cavity-mediated potential is periodic and, in the configurations we consider, its periodicity is double the lattice spacing. Depending on the frequency detuning between atom and cavity, the cavity-mediated potential is described either by density-density interactions, or by global correlated hopping between lattice sites, or by the sum of the two.
We first consider the regime where global correlated hopping is dominant. We use DMRG to study the quantum phases of a one-dimensional lattice at half filling and show that quantum interference between single-particle tunnelling and global interactions give rise to a self-organized topological insulator. The onset of quantum interference leads to spontaneous breaking of the lattice translational symmetry, the corresponding phase resembles nontrivial states of the celebrated Su-Schriefer-Heeger model. Nevertheless, here it arises from an interference phenomenon that has no known fermionic analog.
We then discuss a two-dimensional lattice in the regime where the global potential gives rise to density-density interactions. The interplay between tunneling, onsite interactions, and the global potential gives rise to a rich ground-state phase diagram, which can exhibit Mott-insulator, superfluid, lattice super solid, and charge-density wave phases. We determine the quantum phase diagram by means of a mean-field ansatz and use a slave boson in order to evaluate the entanglement-entropy, the physical spectrum and corresponding entanglement spectrum in the different phases. We probe the scaling of entanglement entropy in the different phases, and discuss in particular on the transition from superfluid to supersolid, which is controlled by the strength of the global interactions.