Energy Spectroscopy of Quantum Critical Points and Non-Equilibrium Dynamics of a Quantum Simulator

Quantum critical points as the transition points between distinct phases of matter are an ever exciting topic in condensed matter physics.They show universal properties such that microscopically different models behave identically at their critical points when they are within the same universality class.One of the main objectives of this thesis is to suggest an alternative approach to characterize universality classes of quantum critical points in two spatial dimensions utilizing the critical torus energy spectrum.After an elementary introduction into quantum spin models, quantum critical points, and the main methods applied within this thesis in Part I, we present our main results in Part II.We, first, analyze the critical torus spectrum of the prototypical transverse field Ising model in Ch. 6, and find that it is given by universal numbers which characterize the universality class and show that it resembles structures of the operator content of the corresponding conformal field theory.We also discuss the influence of fractionalized particles undergoing the Ising transition, and compute the critical torus spectrum for such an Ising* critical point.We then explore the critical torus spectra of the O(N ) universality classes for N ≤ 3 in Ch. 7, before we demonstrate in Ch. 8 that, among other phase transition types, emergent XY*/O(2)* criticality, with a characteristic torus spectrum, is observed for the transition between a Z 2 topologically ordered and a Z 2 symmetry broken phase.The critical torus energy spectrum of critical points involving Dirac fermions is studied in Ch. 9 in the context of a Chiral-Ising Gross-Neveu-Yukawa transition of spinless fermions on different lattices.The fermionic degrees of freedom are found to create a particularly characteristic spectrum which is very different from the standard Ising spectrum.Finally, we explore features of the non-equilibrium dynamics of a Rydberg quantum simulator in Ch. 10.We investigate the properties of finite-time ramps of external parameters with regards to the phase diagram and the total duration of the ramps, and provide a description of observed correlation structures in terms of a short-time expansion of the evolution operator.Additionally, we propose a phenomenological dissipation model showing a very good agreement between numerical simulations and experiments.iii Zusammenfassung Quantenkritische Punkte an Übergängen zwischen unterschiedlichen Phasen sind noch immer ein interessanter Forschungsbereich in der Physik der kondensierten Materie.Sie zeigen universelle Eigenschaften, insofern, dass sich mikroskopisch deutlich unterschiedliche Systeme an ihren kritischen Punkten identisch verhalten, wenn diese in dieselbe Universalitätsklasse fallen.Eines der Ziele dieser Dissertation ist es, das kritische Torus-Energiespektrum als eine alternative Methode zur Charakterisierung von Universalitätsklassen quantenkritischer Punkte in zwei räumlichen Dimensionen vorzuschlagen.Nach einer vorbereitenden Einführung in Quantenspinsysteme, quantenkritische Punkte, und in die Methoden, die in dieser Dissertation verwendet werden, in Teil I, stellen wir die in dieser Dissertation erzielten Ergebnisse in Teil II vor.Zuerst untersuchen wir in Kapitel 6 das kritische Torus-Spektrum des Ising-Modells in transversem Feld, ein Standardbeispiel für kritische Phänomene.Wir zeigen, dass es aus universellen Zahlen zusammengesetzt ist, die die Universalitätsklasse charakterisieren und strukturelle Ähnlichkeiten mit dem Operatorinhalt der zugehörigen konformen Feldtheorie aufweisen.Außerdem diskutieren wir die Veränderungen des Torus-Spektrums, wenn sich fraktionale Teilchen dem klassischen Phasenübergang unterziehen, und berechnen damit das Torus-Spektrum für die Ising* Universalitätsklasse. Anschließend untersuchen wir in Kapitel 7 die kritischen Torus-Spektren der O(N ) Universalitätsklassen für N ≤ 3, bevor wir in Kapitel 8 zeigen, dass der Phasenübergang zwischen einer Z 2 topologisch geordneten und einer Z 2 symmetriegebrochenen Phase, unter anderem, emergente O(2)*/XY* Universalität aufweist, und bestimmen deren charakteristisches Torus-Spektrum.In Kapitel 9 analysieren wir das kritische Torus-Spektrum für kritische Punkte mit Dirac Fermionen im Kontext der chiralen Ising Gross-Neveu-Yukawa Theorie.Die fermionischen Freiheitsgrade erzeugen ein besonders charakteristisches Spektrum, das sich stark vom gewöhnlichen Ising Spektrum unterscheidet.Schlussendlich betracthen wir Eigenschaften der Nichtgleichgewichtsdynamik eines Rydberg Quantensimulators in Kapitel 10.Dabei untersuchen wir das Verhalten einer Dynamik mit zeitabhängigen Parametern in Bezug auf das Phasendiagram und die Zeitdauer.Zudem erklären wir beobachtete Strukturen von Korrelationsfunktionen anhand einer Entwicklung des Zeitentwicklungsoperators für kurze Zeiten, und schlagen ein phänomenologisches Dissipationsmodell vor, das eine sehr gute Übereinstimmung zwischen den numerischen Simulationen und dem Experiment aufweist.v It is a great pleasure for me to express my gratitude to all my friends and associates who (partly) accompanied my journey of performing doctoral studies and made these last five years such an enjoyable and rewarding time.First, I would like to thank my supervisor, Andreas Läuchli, for giving me the chance to join his scientific group and accepting me as his PhD student.I am very grateful for his continuing support and advice throughout my studies, and very much appreciate the interesting projects he pointed out to me, which led me deeper into the exciting world of condensed matter physics.I highly acknowledge our frequent discussions with and without other collaborators and enjoyed the group's other activities, such as the group retreats.Above all, I want to thank Andreas for his ever friendly and welcoming attitude!The wonderful people in the Läuchli group made my time at the Institute for Theoretical Physics especially enjoyful.It was very delightful to share an office with Alexander Wietek for such a long time and with Clemens Ganahl latter during my studies.I have profited a lot from the many discussions and joint software development, and very much appreciate the interesting conversations and fun activities, such as the frequent lunch-time games, which were not directly related to physics.In particular, I would also like to thank Louis-Paul Henry for working together on many projects, which have always been a great pleasure for me, and for his good advice, support, and friendship throughout all the years.I also want to express my gratitude to Christian Romen, Carlo Krimphoff, Thomas Lang, Michael Rader, Elke Stenico, and the other (former) members of the Läuchli group for such a lot of things, which, to keep it short, should not be detailed here.I am especially grateful for the unconditional support from my brother Thomas, my sister Elena, and in particular from my parents, who made all of this possible and were never short of help and understanding.Above all, I would like to thank my wife-to-

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.