Quantum phase transitions in the Spin-Orbit-Coupled extended Bose-Hubbard model

The Bose-Hubbard model has a variety of intriguing ground states and exhibits quantum phase transitions between them, most notably the Mott-insulator–superfluid phase transition. The extended Bose-Hubbard model, which also takes into account nearest-neighbour interactions in addition to the on-site interaction, exhibits even more exotic phases such as super-solid and density-wave states. In the other hand, including a spin-orbit coupling in the (two- component) spinor Bose-Hubbard model gives rise to a twisted superfluid order parameter. In this talk we present phase diagrams and quantum phase transitions in the spin-orbit-coupled extended Bose-Hubbard model, obtained via perturbative and numerical mean-field theory.