Exploring the phase diagram for two-component Bose-Hubbard model in 2D: Mott Insulator to Superfluid transitions and exotic magnetic-like phases

In this dissertation I present results for Bose-Hubbard model in 2D obtained with quantum Monte Carlo simulations by the Worm algorithm and Mean Field techniques. First I study a uniform system and I describe how the Mottinsulator-to-superfluid transition for a majority component is affected by the presence of a minority superfluid one. Then I focus on magnetic-like ground states known as checkerboard phase which can be obtained in the strongly interacting regime. I am able to establish constraints on parameters relevant for experimental setups which allows the considered phase to manifest.