A Unitary Perturbation Theory Approach to Real-Time Evolution in the Hubbard Model
von Manuel Kreye
Datum der mündl. Prüfung:2019-10-23
Erschienen:2019-10-29
Betreuer:Prof. Dr. Stefan Kehrein
Gutachter:Prof. Dr. Stefan Kehrein
Gutachter:Prof. Dr. Laura Covi
Dateien
Name:thesis_web.pdf
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Format:PDF
Zusammenfassung
Englisch
We advance perturbative approaches for out-of-equilibrium quantum many-body systems by applying unitary perturbation theory to the real-time evolution of the weakly interacting Hubbard model in d > 1 dimensions. We derive general expressions for the fermionic operators that allow us to perturbatively calculate the time evolution of observables to second-order expansion in the interaction strength. We find that the results are stable up to and including the prethermalization regime. We apply our findings to the nonequilibrium build-up of density-density correlations after a weak interaction quench and compare the prethermalization values to equilibrium correlations. Furthermore, we analyze the light-cone-like structure of the density-density susceptibility and the equal-time correlation function in the context of the Lieb-Robinson bounds.
Keywords: quantum many-body systems; nonequilibrium dynamics; prethermalization; density-density correlations; Hubbard model; unitary perturbation theory; flow equations