Gneist, Nico (2022). Competing Orders in the Triangular Lattice Hubbard Model, an Application of the Truncated-Unity Functional Renormalization Group. PhD thesis, Universität zu Köln.

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In this PhD thesis, we present and implement the recently developed truncated-unity functional renormalization group (TUFRG) for a set of different triangular lattice Hubbard models around Van Hove filling. In the first part, we will present a brief introduction to the general nature of emerging electronic instabilities in correlated fermion systems. To this purpose, we introduce the Hubbard model as paradigmatic description of correlated electrons in solid state physics and derive first insights about the onset of magnetic and superconductive instabilities in terms of perturbation theory. It will become apparent that already the kinetic part of the Hamiltonian encodes crucial information about these electronic instabilities which are finally triggered by interactions. Nevertheless, we will demonstrate that perturbation theory alone cannot explain the occurrence of unconventional superconductivity which directly establishes the necessity to develop renormalization group methods in the following section. In the second part, we will introduce the TUFRG as a novel form of the functional renormalization group (FRG). The TUFRG advances the FRG in interpretability by introducing a channel decomposition such that several diagrams of the FRG scheme are directly linked to the possibility of certain instabilities. Moreover, it greatly increases the numerical performance of previous FRG schemes by the identification of unimportant momentum dependencies which are subsequently developed in form factors to generate computational speedup. We will not only derive the complete TUFRG framework from first principles, but also demonstrate the details of the numerical implementation. The third part consists of the application of the TUFRG to three different triangular lattice Hubbard systems: a model with SU(2) invariance, a spinless model and a model without SU(2)-invariance. We will employ the TUFRG approach to resolve various instabilities towards magnetism and unconventional superconductivity around Van Hove filling. The models are related to twisted transition metal dichalcogenides (tTMDs), a type of novel Moiré materials. The soundness of the achieved results is complemented with numerical benchmarks and analytical checks.

Item Type: Thesis (PhD thesis)
CreatorsEmailORCIDORCID Put Code
URN: urn:nbn:de:hbz:38-640028
Date: 27 October 2022
Language: English
Faculty: Faculty of Mathematics and Natural Sciences
Divisions: Faculty of Mathematics and Natural Sciences > Department of Physics > Institute for Theoretical Physics
Subjects: Physics
Uncontrolled Keywords:
Functional Renormalization GroupEnglish
Strongly Correlated ElectronsUNSPECIFIED
Unconventional SuperconductivityUNSPECIFIED
Date of oral exam: 19 October 2022
NameAcademic Title
Scherer, MichaelProf. Dr.
Refereed: Yes


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