Strong Correlation Effects in Bosonic and Fermionic Systems Through an Unbiased Quantum Monte Carlo Approach

Sammanfattning: Strongly interacting many-body quantum systems constitute some of the most challenging problems in physics, and exact analytical solutions are rare. In this thesis, we will investigate the models of two such systems numerically using the unbiased worm-algorithm Monte Carlo method.The first model is the t-J model, which describes strongly correlated lattice electrons and is thought to capture the essential physics of high-temperature superconductors. Of particular interest to us is the emergent magnetic polaron studied in the first two papers. The microscopic pairing mechanism between these quasiparticles remains one of the most outstanding open questions in condensed matter physics.The second model is an extended multi-component Bose--Hubbard model, which describes lattice bosons of multiple species. This model is essential to the third paper, in which we demonstrate a novel superfluid phenomenon in the form of a dissipationless drag effect that couples the different superfluid components of a superfluid mixture in a noncollinear fashion. Dissipationless drag is a fundamental effect present in a diverse set of physical systems. In the fourth paper, we further use the Bose--Hubbard model to study other new superfluid phenomena that arise when the number of superfluid components is increased.A general introduction to the research field is first given in the thesis, after which some prerequisites are refreshed. Then essential concepts are introduced, and the numerical method is outlined and benchmarked. Following that is a summary of the research carried out.