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leporello #19
(2024)
Uni-Highlights Januar 2024 : Einladungen zu ausgewählten Veranstaltungen der Goethe-Universität
(2024)
SAFE Update February 2024
(2024)
This thesis contains three theoretical works about certain aspects of the interplay of electronic correlations and topology in the Hubbard model.
In the first part of this thesis, the applicability of elementary band representations (EBRs) to diagnose interacting topological phases, that are protected by spatial symmetries and time-reversal-symmetry, in terms of their single-particle Matsubara Green’s functions is investigated. EBRs for the Matsubara Green’s function in the zero-temperature limit can be defined via the topological Hamiltonian. It is found that the Green’s function EBR classification can only change by (i) a gap closing in the spectral function at zero frequency, (ii) the Green’s function becoming singular i.e. having a zero eigenvalue at zero frequency or (iii) the Green’s function breaking a protecting symmetry. As an example, the use of the EBRs for Matsubara Green’s functions is demonstrated on the Su-Schriefer-Heeger model with exact diagonalization.
In the second part the Two-Particle Self-Consistent approach (TPSC) is extended to include spin-orbit coupling (SOC). Time-reversal symmetry, that is preserved in the presence of SOC, is used to derive new TPSC self-consistency equations including SOC. SOC breaks spin rotation symmetry which leads to a coupling of spin and charge channel. The local and constant TPSC vertex then consists of three spin vertices and one charge vertex. As a test case to study the interplay of Hubbard interaction and SOC, the Kane-Mele-Hubbard model is studied. The antiferromagnetic spin fluctuations are the leading instability which confirms that the Kane-Mele-Hubbard model is an XY antiferromagnet at zero temperature. Mixed spin-charge fluctuations are found to be small. Moreover, it is found that the transversal spin vertices are more strongly renormalized than the longitudinal spin vertex, SOC leads to a decrease of antiferromagnetic spin fluctuations and the self-energy shows dispersion and sharp features in momentum space close to the phase transition.
In the third part TPSC with SOC is used to calculate the spin Hall conductivity in the Kane-Mele-Hubbard model at finite temperature. The spin Hall conductivity is calculated once using the conductivity bubble and once including vertex corrections. Vertex corrections for the spin Hall conductivity within TPSC corresponds to the analogues of the Maki-Thompson contributions which physically correspond to the excitation and reabsorption of a spin, a charge or a mixed spin-charge excitation by an electron. At all temperatures, the vertex corrections show a large contribution in the vicinity of the phase transition to the XY antiferromagnet where antiferromagnetic spin fluctuations are large. It is found that vertex corrections are crucial to recover the quantized value of −2e^2/h in the zero-temperature limit. Further, at non-zero temperature, increasing the Hubbard interaction leads to a decrease of the spin Hall conductivity. The results indicate that scattering of electrons off antiferromagnetic spin fluctuations renormalize the band gap. Decreasing the gap can be interpreted as an effective increase of temperature leading to a decrease of the spin Hall conductivity.
Highlights
• Three ecological groups were identified based on distributional patterns.
• Old assessments were confirmed with the latest occurrence data.
• For each group, we derived different population trends in times of global change.
• Global change elevates importance of vector-borne diseases.
• Our results serve as base for effective Simuliidae monitoring.
Abstract
The black fly genus Simulium includes medically and ecologically important species, characterized by a wide variation of ecological niches largely determining their distributional patterns. In a rapidly changing environment, species-specific niche characteristics determine whether a species benefits or not. With aquatic egg, larval and pupal stages followed by a terrestrial adult phase, their spatial arrangements depend upon the interplay of aquatic conditions and climatic-landscape parameters in the terrestrial realm. The aim of this study was to enhance the understanding of the distributional patterns among Simulium species and their ecological drivers. In an ecological niche modelling approach, we focused on 12 common black fly species with different ecological requirements. Our modelling was based on available distribution data along with five stream variables describing the climatic, land-cover, and topographic conditions of river catchments. The modelled freshwater habitat suitability was spatially interpolated to derive an estimate of the adult black flies' probability of occurrence. Based on similarities in the spatial patterns of modelled habitat suitability we were able to identify three biogeographical groups, which allows us to confirm old assessments with current occurrence data: (A) montane species, (B) broad range species and (C) lowland species. The five veterinary and human medical relevant species Simulium equinum, S. erythrocephalum, S. lineatum, S. ornatum and S. reptans are mainly classified in the lowland species group. In the course of climatic changes, it is expected that biocoenosis will slightly shift towards upstream regions, so that the lowland group will presumably emerge as the winner. This is mainly explained by wider ecological niches, including a higher temperature tolerance and tolerance to various pollutants. In conclusion, these findings have significant implications for human and animal health. As exposure to relevant Simulium species increases, it becomes imperative to remain vigilant, particularly in investigating the potential transmission of pathogens.