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Magnetism is a phenomenon ubiquitously found in everyday life. Yet, together with superconductivity and superfluidity, it is among the few macroscopically realized quantum states. Although well-understood on a quasi-classical level, its microscopic description is still far from being solved. The interplay of strong interactions present in magnetic condensed-matter systems and the non-trivial commutator structure governing the underlying spin algebra prevents most conventional approaches in solid-state theory to be applied.
On the other hand, the quantum limit of magnetic systems is fertile land for the development of exotic phases of matter called spin-liquids. In these states, quantum fluctuations inhibit the formation of magnetic long-range order down to the lowest temperatures. From a theoretical point of view, spin-liquids open up the possibility to study their exotic properties, such as fractionalized excitations and emergent gauge fields. However, despite huge theoretical and experimental efforts, no material realizing spin-liquid properties has been unambiguously identified with a three-dimensional crystal structure. The search for such a realization is hindered by the inherent difficulty even for model calculations. As most numerical techniques are not applicable due to the interaction structure and dimensionality of these systems, a methodological gap has to be filled.
In this thesis, to fill this void, we employ the pseudo-fermion functional renormalization group (PFFRG), which provides a scheme to investigate ground state properties of quantum magnetic systems even in three spatial dimensions.
We report the status quo of this established method and extend it by alleviating some of its inherent approximations. To this end, we develop a multi-loop formulation of PFFRG, including hitherto neglected terms in the underlying flow equations consistently, rendering the outcome equivalent to a parquet approximation. As a necessary prerequisite, we also significantly improve the numerical accuracy of our implementation of the method by switching to a formulation respecting the asymptotic behavior of the vertex functions as well as employing state-of-the-art numerical algorithms tailored towards PFFRG. The resulting codebase was made publicly accessible in the open-source code PFFRGSolver.jl.
We subsequently apply the technique to both model systems and real materials. Augmented by a classical analysis of the respective models, we scan the phase diagram of the three-dimensional body-centered cubic lattice up to third-nearest neighbor coupling and the Pyrochlore lattice up to second-nearest neighbor. In both systems, we uncover in addition to the classically ordered phases, an extended parameter regime, where a quantum paramagnetic phase appears, giving rise to the possibility of a quantum spin liquid.
Additionally, we also use the nearest-neighbor antiferromagnet on the Pyrochlore lattice as well as the simple cubic lattice with first- and third-nearest neighbor couplings as a testbed for multi-loop PFFRG, demonstrating, that the inclusion of higher loop orders has quantitative effects in paramagnetic regimes and that the onset of order can be signaled by a lack of loop convergence.
Turning towards material realizations, we investigate the diamond lattice compound MnSc\(_2\)S\(_4\), explaining on grounds of ab initio couplings the emergence of a spiral spin liquid at low temperatures, but above the ordering transition.
In the Pyrochlore compound Lu\(_2\)Mo\(_2\)O\(_5\)N\(_2\), which is known to not magnetically order down to lowest temperatures, we predict a spin liquid state displaying a characteristic gearwheel pattern in the spin structure factor.
Copy number variations (CNVs) of the KITLG gene seem to be involved in the oncogenesis of digital squamous cell carcinoma (dSCC). The aims of this study were (1) to investigate KITLG CNV in giant (GS), standard (SS), and miniature (MS) schnauzers and (2) to compare KITLG CNV between black GS with and without dSCC. Blood samples from black GS (22 with and 17 without dSCC), black SS (18 with and 4 without dSSC; 5 unknown), and 50 MS (unknown dSSC status and coat colour) were analysed by digital droplet PCR. The results are that (1) most dogs had a copy number (CN) value > 4 (range 2.5–7.6) with no significant differences between GS, SS, and MS, and (2) the CN value in black GS with dSCC was significantly higher than in those without dSCC (p = 0.02). CN values > 5.8 indicate a significantly increased risk for dSCC, while CN values < 4.7 suggest a reduced risk for dSCC (grey area: 4.7–5.8). Diagnostic testing for KITLG CNV may sensitise owners to the individual risk of their black GS for dSCC. Further studies should investigate the relevance of KITLG CNV in SS and the protective effects in MS, who rarely suffer from dSCC.
Dark-haired dogs are predisposed to the development of digital squamous cell carcinoma (DSCC). This may potentially suggest an underlying genetic predisposition not yet completely elucidated. Some authors have suggested a potential correlation between the number of copies KIT Ligand (KITLG) and the predisposition of dogs to DSCC, containing a higher number of copies in those affected by the neoplasm. In this study, the aim was to evaluate a potential correlation between the number of copies of the KITLG and the histological grade of malignancy in dogs with DSCC. For this, 72 paraffin-embedded DSCCs with paired whole blood samples of 70 different dogs were included and grouped according to their haircoat color as follow: Group 0/unknown haircoat color (n = 11); Group 1.a/black non-Schnauzers (n = 15); group 1.b/black Schnauzers (n = 33); group 1.c/black and tan dogs (n = 7); group 2/tan animals (n = 4). The DSCCs were histologically graded. Additionally, KITLG Copy Number Variation (CNV) was determined by ddPCR. A significant correlation was observed between KITLG copy number and the histological grade and score value. This finding may suggest a possible factor for the development of canine DSCC, thus potentially having an impact on personalized veterinary oncological strategies and breeding programs.
Grading, immunohistochemistry and c-kit mutation status are criteria for assessing the prognosis and therapeutic options of canine cutaneous mast cell tumours (MCTs). As a subset, canine digital MCTs have rarely been explored in this context. Therefore, in this retrospective study, 68 paraffin-embedded canine digital MCTs were analysed, and histological grading was assessed according to Patnaik and Kiupel. The immunohistochemical markers KIT and Ki67 were used, as well as polymerase chain reaction (PCR) for mutational screening in c-kit exons 8, 9, 11 and 14. Patnaik grading resulted in 22.1% grade I, 67.6% grade II and 10.3% grade III tumours. Some 86.8% of the digital MCTs were Kiupel low-grade. Aberrant KIT staining patterns II and III were found in 58.8%, and a count of more than 23 Ki67-positive cells in 52.3% of the cases. Both parameters were significantly associated with an internal tandem duplication (ITD) in c-kit exon 11 (12.7%). French Bulldogs, which tend to form well-differentiated cutaneous MCTs, had a higher proportion of digital high-grade MCTs and ITD in c-kit exon 11 compared with mongrels. Due to its retrospective nature, this study did not allow for an analysis of survival data. Nevertheless, it may contribute to the targeted characterisation of digital MCTs.
Fungal infections are a major global health burden where Candida albicans is among the most common fungal pathogen in humans and is a common cause of invasive candidiasis. Fungal phenotypes, such as those related to morphology, proliferation and virulence are mainly driven by gene expression, which is primarily regulated by kinase signaling cascades. Serine-arginine (SR) protein kinases are highly conserved among eukaryotes and are involved in major transcriptional processes in human and S. cerevisiae. Candida albicans harbors two SR protein kinases, while Sky2 is important for metabolic adaptation, Sky1 has similar functions as in S. cerevisiae. To investigate the role of these SR kinases for the regulation of transcriptional responses in C. albicans, we performed RNA sequencing of sky1Δ and sky2Δ and integrated a comprehensive phosphoproteome dataset of these mutants. Using a Systems Biology approach, we study transcriptional regulation in the context of kinase signaling networks. Transcriptomic enrichment analysis indicates that pathways involved in the regulation of gene expression are downregulated and mitochondrial processes are upregulated in sky1Δ. In sky2Δ, primarily metabolic processes are affected, especially for arginine, and we observed that arginine-induced hyphae formation is impaired in sky2Δ. In addition, our analysis identifies several transcription factors as potential drivers of the transcriptional response. Among these, a core set is shared between both kinase knockouts, but it appears to regulate different subsets of target genes. To elucidate these diverse regulatory patterns, we created network modules by integrating the data of site-specific protein phosphorylation and gene expression with kinase-substrate predictions and protein-protein interactions. These integrated signaling modules reveal shared parts but also highlight specific patterns characteristic for each kinase. Interestingly, the modules contain many proteins involved in fungal morphogenesis and stress response. Accordingly, experimental phenotyping shows a higher resistance to Hygromycin B for sky1Δ. Thus, our study demonstrates that a combination of computational approaches with integration of experimental data can offer a new systems biological perspective on the complex network of signaling and transcription. With that, the investigation of the interface between signaling and transcriptional regulation in C. albicans provides a deeper insight into how cellular mechanisms can shape the phenotype.