Transport and diffusion of charge, spin, and heat in the two dimensional Hubbard modelUlaga, Martin (Avtor) Kokalj, Jure (Mentor) Mravlje, Jernej (Komentor) electronic correlationsHubbard modelHeisenberg modeltransportbad metalspin bad metalspin diffusionheat diffusionthermoelectric effectLorenz number.This thesis addresses transport questions in strongly correlated electronic systems in two dimensions. The primary tool for the analysis is the exact numerical treatment of the problem on small clusters, which allows for a description of transport at high temperatures, combined with dynamical mean-field theory and phenomenological approaches. The high-temperature regime under consideration primarily concerns temperatures above the melting point of most materials, but is the natural operating grounds of quantum simulators based on cold atomic gases in optical lattices. We calculate the spin diffusion constant at high temperatures and compare the results with just such an experiment, reproducing the disagreement between theory and experiment in the process. As a possible cause for this discrepancy, we study the spin thermoelectric effect and find it is enhanced in the presence of strong correlations, leading to the mixing of spin and heat transport. We also calculate the ordinary thermoelectric effect and estimate its contribution to the transport of heat. We evaluate the ratio between heat and charge conductivity which at the lowest reachable temperatures indicates the restoration of the Wiedemann-Franz law in the strongly correlated system. We develop a theoretical framework for estimating the influence of the thermoelectric effect on a diffusion experiment following a quench in a quantum simulator and observe the development of an additional long timescale.20242024-01-14 08:15:04Doktorsko delo/naloga153547sl