Transport in one-dimensional quantum systemsLjubotina, Marko (Avtor) Žnidarič, Marko (Mentor) Transportspin chainsintegrabilitydisorderballistic transportsuperdiffusiondiffusionquasiperiodicityFloquetDrude weightdefectIn this thesis we present research on one-dimensional quantum systems performed using a combination of numerical and analytic techniques, with a particular focus on spin transport. We first review the numeric and analytic methods used in our works and present some of the useful tricks we have employed throughout the work. We begin by studying integrable systems, more precisely we study the paradigmatic Heisenberg model. Using tensor network algorithms we study both low and high temperature physics in the model and observe a lack of ballistic transport in the gapped regime. Additionally, at the SU(2) symmetric point we find transport to be superdiffusive with the spin-spin correlation function showing Kardar-Parisi-Zhang scaling. We then move on to discrete time integrable models by studying the integrable Trotterisation of the Heisenberg model.This allows for easier numeric simulations, which enables us to observe Kardar-Parisi-Zhang physics in another clean quantum system. Additionally, we then focus on the ballistic regime of the model, where we employ the Mazur lower bound for the Drude weight using quasilocal conserved charges, and find that it exhibits fractal behaviour. Our focus then drifts away from integrability into more generic systems. We begin by studying a free model with a single perturbed link. In the first case we study a non-interacting perturbation, which allows us to complement our numerical results with analytics, as the model remains free. We show that in the presence of a single link perturbation transport remains ballistic. Numerically we can expand this to the case where the perturbation is interacting and the complete model is no longer integrable. Lastly, we study the effects of breaking the integrability globally by imposing either a random or quasiperiodic field. We observe that the quasiperiodic model's behaviour is qualitatively different from that of the random field model when interactions are turned on. By studying the single particle resonances of the model we find a Fibonacci structure inherent to the quasiperiodic model. Breaking the quasiperiodicity even slightly destroys this structure and suggests a possible avenue to transport engineering in interacting quantum systems.20202020-09-20 08:15:25Doktorsko delo/naloga120461VisID: 110969COBISS_ID: 31334403sl