Dynamic mean-field theory for simulating the infinite-temperature dynamics of spin ensembles
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Date
2024
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Die Hochtemperaturdynamik von Spinsystemen ist für einige moderne Forschungsbereiche wie zum Beispiel Stickstoff-Fehlstellen-Zentren in Diamant oder Kernspinresonanz zentral. Diese theoretische Doktorarbeit befasst sich mit einer dynamischen Molekularfeldtheorie, genannt spinDMFT, mit welcher solche Systeme simuliert werden können. Der geringe numerische Aufwand der Methode erlaubt eine systematische Erweiterung auf Spincluster (CspinDMFT), was die Genauigkeit, allerdings auch den numerischen Aufwand, erhöht. Mit Hilfe von CspinDMFT wird die Dynamik von räumlich ungeordneten Defektspins auf einer Diamantoberfläche simuliert. Das Zusammenspiel von effektiver dipolarer Anisotropie und räumlicher Unordnung führt zu einem erheblichen Unterschied zwischen den Zeitskalen der longitudinalen und transversalen Relaxation. Dieses Phänomen ist auch experimentell beobachtet worden. In einem weiteren Teil dieser Arbeit werden spinDMFT und eine Erweiterung auf nicht-lokale Korrelationen (nl-spinDMFT) verwendet, um Kernspinresonanzmessungen wie zum Beispiel den freien Induktionszerfall oder Spinechos zu simulieren. Die Übereinstimmung mit experimentellen Daten für Kalziumfluorid (CaF$_2$) und Adamantan (C$_10$H$_16$) ist hervorragend. Ein interessanter Ausblick in diesem Kontext ist die Erweiterung auf Magic-Angle-Spinning Experimente, die heutzutage sehr relevant für die Festkörper-Kernspinresonanzspektroskopie mit hoher Präzision sind. Die zentrale Schlussfolgerung dieser Arbeit ist, dass spinDMFT einschließlich der Erweiterungen zwar auf hohe Temperaturen beschränkt sind, in diesem Grenzfall aber numerisch günstige und sehr flexible Methoden darstellen, die auf viele Systeme anwendbar sind.
The high-temperature dynamics of spin systems is crucial in a number of modern research areas such as nitrogen-vacancy centers in diamond and nuclear magnetic resonance. This doctoral thesis deals with a dynamic mean-field theory, dubbed spinDMFT, that allows for the simulation of such systems. The relatively modest computational expense of the method permits an extension to spin clusters (CspinDMFT), which increases both the accuracy and the computational effort. CspinDMFT is employed to simulate the dynamics of randomly-distributed defect spins on a diamond surface. The interplay between effective dipolar anisotropy and positional disorder results in a significant difference between the timescales of longitudinal and transverse relaxation. This phenomenon has also been observed experimentally. In another part of this work, spinDMFT and an extension to non-local correlations (nl-spinDMFT) are used to simulate nuclear magnetic resonance experiments such as the free induction decay and spin echoes. The agreement with experimental data for calcium fluoride (CaF$_2$) and adamantane (C$_10$H$_16$) is excellent. An interesting outlook in this context is the extension to magic-angle-spinning experiments which are highly relevant in solid-state nuclear magnetic resonance spectroscopy with high precision. The central conclusion of this thesis is that spinDMFT and its extensions are limited to high temperatures, but offer computationally cheap and highly flexible numerical methods which are applicable to a wide range of systems in this limit.
The high-temperature dynamics of spin systems is crucial in a number of modern research areas such as nitrogen-vacancy centers in diamond and nuclear magnetic resonance. This doctoral thesis deals with a dynamic mean-field theory, dubbed spinDMFT, that allows for the simulation of such systems. The relatively modest computational expense of the method permits an extension to spin clusters (CspinDMFT), which increases both the accuracy and the computational effort. CspinDMFT is employed to simulate the dynamics of randomly-distributed defect spins on a diamond surface. The interplay between effective dipolar anisotropy and positional disorder results in a significant difference between the timescales of longitudinal and transverse relaxation. This phenomenon has also been observed experimentally. In another part of this work, spinDMFT and an extension to non-local correlations (nl-spinDMFT) are used to simulate nuclear magnetic resonance experiments such as the free induction decay and spin echoes. The agreement with experimental data for calcium fluoride (CaF$_2$) and adamantane (C$_10$H$_16$) is excellent. An interesting outlook in this context is the extension to magic-angle-spinning experiments which are highly relevant in solid-state nuclear magnetic resonance spectroscopy with high precision. The central conclusion of this thesis is that spinDMFT and its extensions are limited to high temperatures, but offer computationally cheap and highly flexible numerical methods which are applicable to a wide range of systems in this limit.
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Dynamic mean-field theory, Disordered spin systems, Nuclear magnetic