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@PHDTHESIS{Profe:974729,
author = {Profe, Jonas Benedikt},
othercontributors = {Kennes, Dante Marvin and Honerkamp, Carsten},
title = {{F}unctional renormalization group developments for
correlations in quantum materials},
school = {RWTH Aachen University},
type = {Dissertation},
address = {Aachen},
publisher = {RWTH Aachen University},
reportid = {RWTH-2023-11581},
pages = {1 Online-Ressource : Illustrationen},
year = {2023},
note = {Veröffentlicht auf dem Publikationsserver der RWTH Aachen
University 2024; Dissertation, RWTH Aachen University, 2023},
abstract = {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 $T_c$ 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.},
cin = {135320 / 130000},
ddc = {530},
cid = {$I:(DE-82)135320_20180927$ / $I:(DE-82)130000_20140620$},
pnm = {DFG project 444137888 - Koordinationsantrag des
Schwerpunktprogramms 2D-Materialien - Die Physik von
van-der-Waals [Hetero-]Strukturen (2DMP) (444137888) / SPP
2244: 2D Materialien – die Physik von van der Waals
[Hetero-]Strukturen (2DMP)},
pid = {G:(GEPRIS)444137888 / G:(GEPRIS)422707584},
typ = {PUB:(DE-HGF)11},
doi = {10.18154/RWTH-2023-11581},
url = {https://publications.rwth-aachen.de/record/974729},
}
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