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%0 Thesis
%A Profe, Jonas Benedikt
%T Functional renormalization group developments for correlations in quantum materials
%I RWTH Aachen University
%V Dissertation
%C Aachen
%M RWTH-2023-11581
%P 1 Online-Ressource : Illustrationen
%D 2023
%Z Veröffentlicht auf dem Publikationsserver der RWTH Aachen University 2024
%Z Dissertation, RWTH Aachen University, 2023
%X In this thesis we derive a unified truncated unity approximation for functional renormalization group and related methods. The approximation is applicable to different materials and models with weak to intermediate correlation strength. First, we introduce the general description of the electronic degrees of freedom, by shortly explaining and deriving the central equations for Density functional theory (DFT). This leads us to the introduction of the tight-binding description of solids for which we state the general type of the kinetic Hamiltonian used throughout this thesis. We follow by a discussion of optical conductivities of tetra layer graphene and argue that for this observable a DFT description is expected to be accurate. We develop a simple model for tetra layer graphene structures based on Density functional theory simulations and compare the results with experimental measurements. Since a DFT is not fully capturing interaction effects, we then introduce the truncated unity Functional renormalization Group (TUFRG)to extend the electronic structure by incorporating more interaction effects. This is done in a self-contained fashion starting from the path integral formulation of the partition function. After deriving the flow equations, we detail the approximations TUFRG introduces and discuss in what sense it is controlled. Next, we derive the TUFRG flow equations and their modifications when choosing a sharp frequency cut off. Here, we discuss different types of symmetries - U(1),SU(2), energy/momentum conservation and point group - detailing how each changes the flow equations. We also discuss a few recently emerging alternative approximation schemes and explain how observables are calculated in this approach. After presenting the formalism, we introduce the diverge code and explain the specific design choices in the implementation of the TUFRG backend. We also present an example how a simulation is performed using the python interface, where we set up a simulation of the model investigated in the next chapter. Finally, we employ the TUFRG for two different problems aiming to understand their superconducting properties. The first problem is a mechanism to study superconductivity in spin-polarized materials with strongly separated bands. This mechanism might be applicable to some dilute superconductors such asZrNCl, WTe2 and a few Moiré materials. We extend the existing studies to different lattices with varying coordination number gauging the applicability of the mechanism to the proposed materials. By establishing the electronic phase diagram for the different cases we estimate the stability of the mechanism. As the second problem we investigate the superconducting order parameter of Sr2RuO4 around which there is a long standing debate. Our calculations are based on ab-initiomodels incorporating different levels of strain on top of which we perform TUFRG. We calculate the phase diagram and analyze T<sub>c</sub> under strain, linking to experiments. We offer a simple explanation for the observed behaviour and compare our results to state-of-the-art dynamical mean-field theory. We discuss the implications of the differences between the two results and argue that theses mall differences will not qualitatively change our conclusions.
%F PUB:(DE-HGF)11
%9 Dissertation / PhD Thesis
%R 10.18154/RWTH-2023-11581
%U https://publications.rwth-aachen.de/record/974729