Monte Carlo Simulations of strongly correlated and frustrated quantum systems

We study the dynamics of the 1D t-J model with nearest neighbor (n.n) interaction at finite doping using the hybrid-loop quantum Monte Carlo. On the basis of the spectral functions of the 1/r(2) t-J model the excitation content for the one- and two-particle spectral functions for the n.n. t-J model are obtained from the Bethe-Ansatz solution and compared with the Monte Carlo results. We find that the procedure describes with extremely hight accuracy the excitation of the n.n. t-J model. We furthermore use quantum Monte Carlo simulations to analyze the phases of ultra-cold bosonic atom gases in optical lattices, in particular in the presence of frustrated and random interaction strength. We find that such systems display interesting quantum phases, such as supersolid and Bose-glass phases, and discuss possible experimental setups to examine such phenomena.