Auswahl der wissenschaftlichen Literatur zum Thema „Topological frustration“

Spin 1/2 quantum spin chains represent the prototypical model for coupled two-level systems. Consequently, they offer a fertile playground for both fundamental and technological applications ranging from the theory of thermalization to quantum computation. Recently, it has been shown that interesting phenomena are associated to the boundary conditions imposed on the quantum spin chains via the so-called topological frustration. In this work, we analyze the effects of such frustration on a few-spin system, with a particular focus on the strong even–odd effects induced in the ground-state energy. We then implement a topologically frustrated quantum spin chain on a quantum computer to show that our predictions are visible on current quantum hardware platforms.

Understanding geometric frustration of ordered phases in two-dimensional condensed matter on curved surfaces is closely related to a host of scientific problems in condensed matter physics and materials science.

L'objectif de ce travail de thèse est de déterminer les lois fondamentales qui décrivent les écoulement de fluides actifs confinés dans des réseaux hydrauliques. Dans la première partie, je détaille les méthodes expérimentales et le système modèle que j'ai instauré. Ensuite, en me focalisant sur les réseaux hydrauliques réguliers de valence impaire, j'établis une analogie directe entre l'hydraulique active et le magnétisme frustré. Je démontre notamment pourquoi les écoulements spontanés des liquides actifs sont généralement dégénérés, caractérisés par des lignes de courant aux géométries auto-similaires. Par une combinaison d'études expérimentales et numériques, je lie la géométrie aléatoire macroscopique des écoulements à la forme microscopique des canaux constituant le réseau hydraulique, proposant ainsi un cadre théorique minimal pour prédire et expliquer la diversité structurale des écoulements. Dans la troisième partie, j'étends les lois de l'hydraulique active à une classe de réseaux plus étendus. Je démontre également comment les motifs d'écoulement sont liés aux conformations de glaces de spins et, de manière plus générale, aux modèles de vertex. Ces correspondances quantitatives permettent une prédiction solide de la géométrie des écoulements, établissant des liens entre des domaines de la physique jusqu'alors distincts. En conclusion, je résume mes résultats et propose un programme de recherche visant à parfaire notre compréhension des écoulements de la matière active dans les réseaux hydrauliques
The aim of this thesis is to determine the fundamental laws that describe the flow of active fluids confined in hydraulic networks. In the first part, I detail the experimental methods and the model system I have established. Then, by focusing on regular hydraulic networks of odd valence, I establish a direct analogy between active hydraulics and frustrated magnetism. In particular, I demonstrate why the spontaneous flows of active liquids are generally degenerate, characterized by streamlines with self-similar geometries. Through a combination of experimental and numerical studies, I link the macroscopic random geometry of the flows to the microscopic shape of the channels constituting the hydraulic network, thus proposing a minimal theoretical framework to predict and explain the structural diversity of the flows. In the third part, I extend the laws of active hydraulics to a broader class of networks. I also demonstrate how flow patterns are related to spin ice configurations and, more generally, to vertex models. These quantitative correspondences allow for a robust prediction of the flow geometry, establishing links between previously distinct areas of physics. In conclusion, I summarize my results and propose a research program aimed at improving our understanding of the flow of active matter in hydraulic networks

À l'aube de la seconde révolution quantique, comprendre et exploiter les phénomènes résultant de l'interaction entre la non-localité intrinsèque de la mécanique quantique et les interactions purement non-locales est d'une importance cruciale pour le développement de nouvelles technologies quantiques. Dans cette thèse, nous nous concentrerons principalement sur les effets non-locaux introduits par la frustration topologique (FT), une forme de frustration faible qui a été introduite pour la première fois dans le contexte des chaînes de spins quantiques antiferromagnétiques en appliquant les conditions aux limites frustrées, réalisées comme une combinaison de conditions aux limites périodiques et d'un nombre impair de spins. Notre objectif est double. D'une part, nous améliorerons la compréhension théorique des phases topologiquement frustrées. Au-delà de ces implications théoriques, ce travail démontrera que les chaînes de spins FT présentent un potentiel technologique convaincant, les proposant comme des candidats compétitifs pour le développement de batteries quantiques robustes et efficaces
At the verge of the second quantum revolution, understanding and exploiting the phenomena resulting from the interplay between the intrinsic non-locality of quantum mechanics and purely non-local interactions is of crucial importance for the development of novel quantum technologies. In this thesis, we will mostly focus on the non-local effects introduced by topological frustration (TF), a form of weak frustration that was first introduced in the context of antiferromagnetic quantum spin chains by applying the so called frustrated boundary conditions, realized as a combination of periodic boundary conditions and odd number of spins. Our goal is double. From one side, we will further improve the theoretical understanding of topologically frustrated phases. Beyond these theoretical implications, this work will demonstrate that TF spin chains exhibit compelling technological potential, proposing them as competitive candidates for the development of robust and efficient quantum batteries

In der eingereichten Dissertation wird eine Reihe von niederdimensionalen und frustrierten magnetischen Systemen mit Hilfe der Elektronenspinresonanz (ESR) untersucht, um deren magnetische Eigenschaften und Wechselwirkungen zu charakterisieren. Sowohl niederdimensionale als auch frustrierte Systeme können exotische magnetische Phänomene zeigen, da es in beiden Fällen trotz starker magnetischer Korrelationen zu einer Unterdrückung von konventioneller langreichweitiger magnetischer Ordnung kommen kann. Auf der anderen Seite sind zweidimensionale Systeme wie Graphen und die damit verwandten topologischen Isolatoren interessant für Anwendungen in der Spintronik oder in Quantencomputern. Über das Einbringen von magnetischer Ordnung soll dabei die Kontrolle über den Spin von Elektronen erlangt werden. Es werden quasieindimensionale Spinketten in Cu(py)2Br2 untersucht, die ein gutes Modellsysteme für den Vergleich mit exakten theoretischen Berechnungen darstellen. Durch eingehende ESR-Messungen ist es gelungen, ein Modell für die Ausrichtung der Anisotropieachse zu entwickeln, die senkrecht zur Kettenachse steht. Zusätzlich zum g-Tensor konnten durch Magnetisierungsmessungen das Austauschintegral und dessen Anisotropie bestimmt werden. Die Austauschwechselwirkung kann über die Substitution von Br- mit Cl-Ionen in Cu(py)2(Cl1-xBrx)2 gezielt variiert werden. Des Weiteren wird eine kombinierte Studie aus STM- und ESR-Untersuchungen an monolagigem Graphen mit induzierten Fehlstellen vorgestellt. Es wurden Defekte durch den Beschuss mit Ar-Ionen in Graphen kontrolliert hergestellt, deren lokale elektronische Eigenschaften sich mit STM- und STS-Messungen charakte-risieren lassen. Mit ESR-Messungen konnte gezeigt werden, dass die an den einzelnen Fehlstellen lokalisierten magnetischen Momente eine dominant antiferromagnetische Austauschwechselwirkung besitzen. Die Charakterisierung der magnetischen Wechselwirkungen zwischen lokalisierten Momenten stand auch für den mit Mn dotierten topologischen Isolator Bi2Te3 im Vordergrund, welcher einen ferromagnetischen Phasenübergang bei tiefen Temperaturen zeigt. Anhand des mit ESR beobachteten Korringa-Verhaltens wurde bewiesen, dass die lokalisierten Mn-Spins an leitende Bänder gekoppelt sind und die ferromagnetische Ordnung folglich per RKKY-Wechselwirkung vermittelt wird. Es wurden kurzreichweitige magnetische Korrelationen in einem ausgedehnten Temperaturbereich oberhalb der Ordnungstemperatur beobachtet, die Hinweise auf einen zweidimensionalen Charakter zeigen. Ausgedehnte Temperaturbereiche mit kurzreichweitigen Korrelationen werden ebenfalls in den untersuchten magnetisch frustrierten Materialien beobachtet. In einer kombinierten Studie aus HF-ESR, NMR und µSR wird die Spindynamik in CoAl2O4 charakterisiert, in dem moderate Unordnung zu einem Verschwimmen der Phasengrenze zwischen Neél-Ordnung und einer Spinflüssigkeit mit spiralförmigen Korrelationen führt. Außerdem werden zwei Vertreter aus der Klasse der Swedenborgite behandelt, in denen die Spinstruktur in YBaCo4O7 durch Substitution modifiziert wird. Ziel ist die Entkopplung der enthaltenen Kagome-Schichten, welche ein zweidimensionales frustriertes System darstellen. In den vorgestellten HF-ESR- und NMR-Messungen beobachtet man ein Spinglasverhalten für YBaCo3AlO7, das aus der Unordnung bei der Besetzung der Gitterplätze resultiert. In YBaCo3FeO7 ist die Unordnung geringer und mit ESR-Untersuchungen konnte gezeigt werden, dass es zu einer effektiven Entkopplung der Fe-Spins zwischen den Kagome-Schichten kommt.

Dans cette thèse, l’étude de plusieurs modèles de systèmes magnétiques frustrés a été couverte. Leur racine commune est le modèle de la glace de spin, qui se transforme en modèle de la glace sur réseau kagome (kagome ice) et réseau en damier (square ice) à deux dimensions, et la chaîne d’Ising à une dimension. Ces modèles ont été particulièrement étudiés dans le contexte de transitions de phases avec un ordre magnétique induit par les contraintes du système : en effet, selon la perturbation envisagée, les contraintes topologiques sous-jacentes peuvent provoquer une transition de Kasteleyn dans le kagome ice, ou une transition de type vitreuse dans la square ice, due à l’émergence d’un ordre ferromagnétique dans une chaîne d’Ising induit seulement par des effets de taille fini. Dans tous les cas, une étude détaillée par simulations numériques de type Monte Carlo ont été comparées à des résultats théoriques pour déterminer les propriétés de ces transitions. Les contraintes topologiques du kagome ice ont requis le développement d’un algorithme de vers permettant aux simulations de ne pas quitter l’ensemble des états fondamentaux. Une revue poussée de la thermodynamique et de la réponse de la diffraction de neutrons sur kagome ice sous un champ magnétique planaire arbitraire, nous ont amené à une compréhension plus profonde de la transition de Kasteleyn, et à un modèle numérique capable de prédire les figures de diffraction de neutrons de matériau de kagome ice dans n’importe quelles conditions expérimentales. Sous certaines conditions, ce modèle a révélé des propriétés thermodynamiques quantifiées et devrait fournir un terreau fertile pour de futurs travaux sur les conséquences des contraintes et transitions de phases topologiques. Une étude combinée du square ice et de la chaîne d’Ising a mise en lumière l’apparition d’un ordre sur réseau potentiellement découplé de l’ordre ferromagnétique sous-jacent, et particulièrement pertinent pour les réseaux magnétiques artificiels obtenus par lithographie
In this thesis a series of model frustrated magnets have been investigated. Their common parent is the spin ice model, which is transformed into the kagome ice and square ice models in two-dimensions, and an Ising spin chain model in one-dimension. These models have been examined with particular interest in the spin ordering transitions induced by constraints on the system: a topological constraint leads, under appropriate conditions, to the Kasteleyn transition in kagome ice and a lattice freezing transition is observed in square ice which is due to a ferromagnetic ordering transition in an Ising chain induced solely by finite size effects. In all cases detailed Monte Carlo computational simulations have been carried out and compared with theoretical expressions to determine the characteristics of these transitions. In order to correctly simulate the kagome ice model a loop update algorithm has been developed which is compatible with the topological constraints in the system and permits the simulation to remain strictly on the groundstate manifold within the appropriate topological sector of the phase space. A thorough survey of the thermodynamic and neutron scattering response of the kagome ice model influenced by an arbitrary in-plane field has led to a deeper understanding of the Kasteleyn transition, and a computational model that can predict neutron scattering patterns for kagome ice materials under any experimental conditions. This model has also been shown to exhibit quantised thermodynamic properties under appropriate conditions and should provide a fertile testing ground for future work on the consequences of topological constraints and topological phase transitions. A combined investigation into the square ice and Ising chain models has revealed ordering behaviour within the lattice that may be decoupled from underlying ferro- magnetic ordering and is particularly relevant to magnetic nanoarrays

Doutoramento em Física
Superconductivity and topology in tight-binding models are two of the most actively researched topics in contemporary condensed matter physics. In this thesis, we aim at presenting a series of original results that encompass both topics while exploring, at the same time, a correspondence that can be drawn between them, highlighting in this process some of their common features and mutual relations. In the context of superconductivity, we focus on the study of frustration effects in systems with multiple superconducting elements. For a frustrated system of three quasi-2D superconducting bands, we construct the in-plane magnetic field versus applied temperature phase diagram and show that there are regions of stable chiral solutions for the superconducting phases, i.e, states where the broken time-reversal symmetry translates into the appearance of persistent supercurrents. We then proceed to study a model of an open chain of superconducting elements with a frustrated unit cell. It is shown that the global superconducting state of the chain can be written as a one-particle state with uniform density in an equivalent tight-binding chain. The appearance (disappearance) of edge supercurrents in this system is related to the closing (opening) of the gap between the energy bands of the corresponding tight-binding chain, which can be indicative of a topological transition. In the context of topological insulators, we focus on many-body states of models with interactions, whose topological characterization is still, to a large extent, an open problem. We begin by addressing the problem of two-hole states in open Su-Schrieffer-Heeger chains with interactions. For strong interactions, the energy spectrum is composed of different subspaces which are classified either as topologically trivial or non-trivial. For a specific subspace, an effective model of one-particle states is constructed and explicitly shown to host topological states. Finally, we study two-body states in periodic Su-Shrieffer-Heeger chains with interactions. When the interactions are strong and of the nearest-neighbor type, a peculiar kind of topological states is found, where the localized behavior is manifested at the edges of the internal coordinate, namely the relative distance between the two particles, making them intrinsically many-body topological states with no counterpart in single-particle states.
Supercondutividade e topologia em modelos tight-binding são dois dos tópicos mais activamente estudados na física da matéria condensada contemporânea. Nesta tese pretendemos apresentar uma série de resultados originais abarcando ambos os tópicos e, simultaneamente, explorar uma correspondência que pode ser estabelecida entre eles, realçando nesse processo algumas das suas características comuns e relações mútuas. No contexto da supercondutividade, focamo-nos no estudo dos efeitos da frustração em sistemas com múltiplos elementos supercondutores. Para um sistema frustrado de três bandas supercondutoras quasi-2D, é demonstrada a existência de regiões no diagrama de fases do campo magnético planar aplicado versus temperatura onde há soluções quirais estáveis para as fases supercondutoras, isto é, estados em que a quebra da simetria de inversão temporal se traduz no aparecimento de supercorrentes persistentes. Procedemos em seguida ao estudo de um modelo de uma cadeia de elementos supercondutores aberta com uma célula unitária frustrada. Mostra-se aí que o estado supercondutor global da cadeia pode ser escrito como um estado de uma partícula com densidade uniforme numa cadeia tight-binding equivalente. O aparecimento (desaparecimento) de supercorrentes fronteiriças neste sistema é relacionado com o fechamento (abertura) do hiato entre as bandas de energia da cadeia tight-binding correspondente, o que pode ser indicativo de uma transição topológica. No contexto de isoladores topológicos, focamo-nos em estados de múltiplas partículas em modelos com interacção, cuja caracterização topológica permanece, em larga medida, uma questão em aberto. Começamos por abordar o problema de estados de duas lacunas em cadeias Su-Schrieffer-Heeger abertas com interacções. Para interacções fortes, o espectro de energia é composto de diferentes subespaços que são classificados como topologicamente triviais ou não-triviais. Para um subespaço específico, é construído um modelo efectivo de estados de uma partícula que se demonstra explicitamente ser capaz de albergar estados topológicos. Finalmente, estudamos estados de duas partículas em cadeias Su-Schrieffer-Heeger periódicas com interacções. Quando as interacções são fortes e do tipo próximos-vizinhos, um tipo peculiar de estados topológicos é encontrado, no qual o comportamento localizado se manifesta nas fronteiras da coordenada interna, nomeadamente a distância relativa entre as duas partículas, o que os torna intrinsecamente estados de múltiplas partículas sem qualquer equivalente em estados de uma partícula.

Proteins are biological macromolecules formed by sequentially joining natural amino acids through peptide bonds. The sequence of amino acids in a protein chain determines its three dimensional structure under physiological conditions. Proteins performdiverse functions such as transporting molecules, transmitting signals between cells, catalyzing metabolic reactions etc. In this thesis I have studied problems related to protein folding, function and aggregation using molecular dynamics simulations and protein models at atomistic and coarse-grained resolution

Abstract Topological tailoring of materials at a micro-scale can achieve a diverse range of extreme physical and mechanical properties. Modification of material properties through customizing the structural pattern paves an avenue for novel functional product design. In this paper, a non-periodic microstructure design framework is explored for functional parts design with high-strength and functional property gradation. To address the common problem of geometric frustration in non-periodic microstructure design, we employ a smooth transition layer to connect distinct structural patterns and thus achieve functional gradation between adjacent microstructures. The concept of spatial control points is introduced for implementing the transition layer. To pursue a superior macro-structural performance for designing objects, we formulate the control point as design variables and encapsulate it into macro-structural design optimization problems. Given that our objective function involves finite element (FE) simulations, a surrogate model-based optimization scheme is utilized to cope with the computational challenge brought by the FE simulation. Experimental results demonstrate that the proposed design framework can yield both functionally graded light-weight structures and high-strength macro-mechanical performance. The compatibility issues in traditional non-periodic microstructure design are addressed. Comparative studies reveal that the proposed framework is robust and can potentially generate desired functional products with spatially varying properties.