08 Fakultät Mathematik und Physik
Permanent URI for this collectionhttps://elib.uni-stuttgart.de/handle/11682/9
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Item Open Access Spin-orbit coupled states arising in the half-filled t2g shell(2023) Schönleber, MarcoStrongly correlated and spin-orbit coupled t2g systems have been extensively investigated. By coupling orbital and spin angular momentum into one quantity, spin-orbit coupling (SOC) tends to reduce orbital degeneracy, e.g. for the widely studied case of one hole in the t2g shell. However, the opposite has to be expected at half filling. Without spin-orbit coupling, all orbitals are half filled, no orbital degree of freedom is left and coupling to the lattice can be expected to be small. At dominant spin-orbit coupling, in contrast, one of the j=3/2 states is empty and the system couples to the lattice. We investigate this issue. One finding is that the low-energy manifold evolves smoothly from the four S=3/2 states in the absence of SOC to the four j=3/2 states with dominant SOC. These four states are always separated from other states by a robust gap. We then discuss a relevant superexchange mechanism to assess the interplay between spin-orbit coupling and coupling to the lattice.Item Open Access Bell-state measurement exceeding 50% success probability with linear optics(2023) Bayerbach, Matthias J.; D’Aurelio, Simone E.; Loock, Peter van; Barz, StefanieItem Open Access Thermodynamical stability analysis of a model quasicrystal(2022) Holzwarth, MoritzThe thermodynamical stability of a simple 2D model quasicrystal is analysed using the theory of the phason elastic free energy. Atoms in the crystal interact via a double-well potential called the Lennard-Jones Gauß-potenital. The essential mechanisms that support the quasicrystal's free energy are atom jumps called phasonic flips. The distribution of such flips in a crystal is computed in dependency of the crystal lattice, which is parameterized by a 2x2-matrix called the phasonic strain. This computation is fully analytic and is based on the popular cut-and-project-scheme for quasicrystals. The quasicrystal is found to be instable at low temperature but stabilized at high temperature due to large entropy. This is in accordance with an MD-simulation from 2008 that used the LJG-Interaction-potential for the first time.Item Open Access Lasertreatment of Al-Cu materials(2023) Kümmel, SimonIn this work, the bond strength and stability of aluminium, copper and their alloys are investigated upon excitation using DFT calculations. In particular, free energy curves, elastic constants and phonon spectra are used to identify changes in the bond strength and the density of states at different degrees of excitation are used to explain the changes. We find nearly no change in bond strength in aluminium, a strong increase in bond strength in copper and bond hardening of certain modes in the AlCu alloys.Item Open Access Quantum algorithms and quantum machine learning for differential equations(2023) Schillo, NiclasThe fast and accurate solution of differential equations is a highly researched topic. Classical methods are able to solve very large systems, however, this can require highperformance computers and very long computational times. Since quantum computers promise significant advantages over classical computers, quantum algorithms for the solution of differential equations have received a lot of attention. Particularly interesting are algorithms that are relevant in the current Noisy-Intermediate-Scale-Quantum (NISQ) era, characterized by small and error-prone systems. In this context, promising candidates are variational quantum algorithms which are hybrid quantumclassical algorithms where only a part of the algorithm is executed on the quantum computer. Thus, they typically require fewer qubits and qubit gates and can tolerate the errors stemming from an imperfect quantum computer. One important example of variational quantum algorithms is the so-called quantum circuit learning (QCL) algorithm, which can be used to approximate functions. Here, an ansatz function is formed with a data encoding layer, subsequently transformed by a shallow parameterized circuit and finally the measurement of an expectation value defines the function value. In this thesis, this method is investigated in great detail, developing new and improved circuit designs and comparing their usefulness in approximating different functions. The method is also tested on a real quantum computer, which has not been reported in literature yet. For this purpose, the algorithm is executed on the superconducting quantum computer IBM Quantum System One in Ehningen to investigate its applicability in the NISQ era. The concept of QCL can be combined with the parameter shift rule to determine derivatives. This enables the solution of nonlinear differential equations. This procedure is subjected to thorough testing across a multitude of differential equations while being compared to other quantum algorithms for solving differential equations. The strengths of this algorithm are shown but also the weaknesses are analyzed. Going beyond the current state of research, the method is extended to solve coupled differential equations with a single circuit, significantly reducing the computational effort. Lastly, a differential equation is successfully solved on the quantum computer IBM Quantum System One in Ehningen.Item Open Access From ground state properties to high energy spectroscopy : extending the application of DMFT for correlated quantum materials(2020) Schmid, Michael; Daghofer, Maria (Prof. Dr.)Strongly correlated electron systems exhibit rich physical phenomena reaching from superconductivity, Kondo- and, Mott physics to novel magnetic phases, which lie beyond most single-particle approaches such as density functional theory (DFT) or static mean-field theory. For many transition metal oxides (TMOs) such as Ca2RuO4 or LiV2O4 this is often a result of the partially filled d shells, leading to many-body wave functions, which cannot expressed as a single-slater determinant. Moreover, within this compounds there is often no clear hierarchy of energy scales, e.g. strong spin-orbit coupling, Hund’s coupling, and crystal-field splitting, making the description with minimal models difficult. The breakdown of the single-particle picture triggered the development of numerous numerical methods (DMFT, DMRG, VCA, . . . ) within the last decades, all aimed at tackling the aforementioned phenomena with complementary approximations. One of the most prominent methods for describing real compounds has become dynamical mean-field theory (DMFT), which in many cases has proven to describe local electronic phenomena in good agreement with experimental results. In this thesis we perform state of the art DFT+DMFT calculations in its single shot approach to complement theoretical k-resolved one-particle spectral functions to neutron and x-ray diffraction experiments on Ca2RuO4 . In the experiment small DC currents were applied to a Ca2RuO4 single-crystal resulting in the stabilization of new nonequilibrium phases. Based on experimentally refined structures, DFT calculations are performed to extract a tight binding model by projecting the correlated t2g -subspace onto maximally localized Wannier orbitals. Within our DMFT calculations spin-orbit coupling (SOC) and the spherical invariant Coulomb interaction are added to calculate spectral functions. The results indicate a semimetalic state with partially gapped Fermi surface in the nonequilibrium phases with elongated RuO6 octahedra. Additionally, we extend the DFT+DMFT scheme by a discretization scheme to obtain core-level spectroscopy data, such as XAS or RIXS spectra. This concept is based on the discretization of the DMFT hybridization function to construct an Anderson impurity model of finite bath sites. The discretized model is then extended by the core levels and core-valence interaction. To include sufficiently large amounts of bath sites, despite using an exact diagonalization (ED) solver, we choose the natural orbital basis as the single particle basis of choice to compute RIXS and XAS spectra.Item Open Access Variational cluster approximation at finite temperatures(2022) Lotze, Jan; Daghofer, Maria (Prof. Dr.)Being able to describe thermodynamics and dynamics of ordered systems at finite temperature allows capturing the signatures of different phases as well as thermal transitions between them. Systems of strongly correlated electrons residing in multiple orbitals where spin-orbit coupling is of significance can exhibit a multitude of exotic phases. Modelling these systems and capturing their properties for the entire temperature range is a non-trivial task. In this thesis, the implementation details of several cluster solvers used for the variational cluster approximation (VCA) at finite temperature are described, since this method is capable of modelling the systems mentioned before while incorporating local quantum fluctuations. The most reliable, sufficiently benchmarked and best performing solver among them is then used to investigate the magnetic and orbital properties of Sr2IrO4 and Ca2RuO4 described by three-band Hubbard models, as well as the Kondo lattice model at half-filling.Item Open Access Simulation studies of selective laser melting(2022) Gorgis, AzadThe technology of SLM is used to layer three-dimensional functional components. Studying and refining the factors that influence the melting of Al layer. The layer is made up of six distinct Al atom sizes in the shape of a sphere (ball) with various diameters (40˚A, 80˚A, 160˚A, 220˚A, 440˚A, 880˚A). The simulation depends mainly on MD to simulate the melting process. Although the sample sizes change, system parameters must be scaled to accommodate two distinct sample sizes. The whole melting of the Al layer has been recorded, using both sample 1 (40˚A, 80˚A, 160˚A) and sample 2 (220˚A, 440˚A, 880˚A), where with and without Ar gas, to explore the influence of Ar in the system. It is expected that the findings of this study will serve as a platform for further research into complex systems with several layers, and that the methodological style used in this work will serve as a model for systematic studies into other structures. In the near future, this research might aid materials design for next-generation in 3D printing.Item Open Access Measurements of entropic uncertainty relations in neutron optics(2020) Demirel, Bülent; Sponar, Stephan; Hasegawa, YujiThe emergence of the uncertainty principle has celebrated its 90th anniversary recently. For this occasion, the latest experimental results of uncertainty relations quantified in terms of Shannon entropies are presented, concentrating only on outcomes in neutron optics. The focus is on the type of measurement uncertainties that describe the inability to obtain the respective individual results from joint measurement statistics. For this purpose, the neutron spin of two non-commuting directions is analyzed. Two sub-categories of measurement uncertainty relations are considered: noise-noise and noise-disturbance uncertainty relations. In the first case, it will be shown that the lowest boundary can be obtained and the uncertainty relations be saturated by implementing a simple positive operator-valued measure (POVM). For the second category, an analysis for projective measurements is made and error correction procedures are presented.Item Open Access Character of doped holes in Nd1-xSrxNiO2(2021) Plienbumrung, Tharathep; Schmid, Michael Thobias; Daghofer, Maria; Oleś, Andrzej M.We investigate charge distribution in the recently discovered high-𝑇𝑐 superconductors, layered nickelates. With increasing value of charge-transfer energy, we observe the expected crossover from the cuprate to the local triplet regime upon hole doping. We find that the 𝑑-𝑝 Coulomb interaction 𝑈𝑑𝑝 makes Zhang-Rice singlets less favorable, while the amplitude of local triplets at Ni ions is enhanced. By investigating the effective two-band model with orbitals of 𝑥2-𝑦2 and s symmetries we show that antiferromagnetic interactions dominate for electron doping. The screened interactions for the s band suggest the importance of rare-earth atoms in superconducting nickelates.
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