@phdthesis{Schrauth2021,
  author    = {Schrauth, Manuel},
  title     = {Critical Phenomena in Topologically Disordered Systems},
  doi       = {10.25972/OPUS-23499},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-234998},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2021},
  abstract  = {Clearly, in nature, but also in technological applications, complex systems built in an entirely ordered and regular fashion are the exception rather than the rule. In this thesis we explore how critical phenomena are influenced by quenched spatial randomness. Specifically, we consider physical systems undergoing a continuous phase transition in the presence of topological disorder, where the underlying structure, on which the system evolves, is given by a non-regular, discrete lattice. We therefore endeavour to achieve a thorough understanding of the interplay between collective dynamics and quenched randomness. According to the intriguing concept of universality, certain laws emerge from collectively behaving many-body systems at criticality, almost regardless of the precise microscopic realization of interactions in those systems. As a consequence, vastly different phenomena show striking similarities at their respective phase transitions. In this dissertation we pursue the question of whether the universal properties of critical phenomena are preserved when the system is subjected to topological perturbations. For this purpose, we perform numerical simulations of several prototypical systems of statistical physics which show a continuous phase transition. In particular, the equilibrium spin-1/2 Ising model and its generalizations represent -- among other applications -- fairly natural approaches to model magnetism in solids, whereas the non-equilibrium contact process serves as a toy model for percolation in porous media and epidemic spreading. Finally, the Manna sandpile model is strongly related to the concept of self-organized criticality, where a complex dynamic system reaches a critical state without fine-tuning of external variables. Our results reveal that the prevailing understanding of the influence of topological randomness on critical phenomena is insufficient. In particular, by considering very specific and newly developed lattice structures, we are able to show that -- contrary to the popular opinion -- spatial correlations in the number of interacting neighbours are not a key measure for predicting whether disorder ultimately alters the behaviour of a given critical system.},
  subject      = {Ising-Modell},
  language  = {en}
}
@phdthesis{Hetterich2018,
  author    = {Hetterich, Daniel Marcus},
  title     = {Localization within disordered systems of star-like topology},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-169318},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2018},
  abstract  = {This Thesis investigates the interplay of a central degree of freedom with an environment. Thereby, the environment is prepared in a localized phase of matter. The long-term aim of this setup is to store quantum information on the central degree of freedom while exploiting the advantages of localized systems. These many-body localized systems fail to equilibrate under the description of thermodynamics, mostly due to disorder. Doing so, they form the most prominent phase of matter that violates the eigenstate thermalization hypothesis. Thus, many-body localized systems preserve information about an initial state until infinite times without the necessity to isolate the system. This unique feature clearly suggests to store quantum information within localized environments, whenever isolation is impracticable. After an introduction to the relevant concepts, this Thesis examines to which extent a localized phase of matter may exist at all if a central degree of freedom dismantles the notion of locality in the first place. To this end, a central spin is coupled to the disordered Heisenberg spin chain, which shows many-body localization. Furthermore, a noninteracting analog describing free fermions is discussed. Therein, an impurity is coupled to an Anderson localized environment. It is found that in both cases, the presence of the central degree of freedom manifests in many properties of the localized environment. However, for a sufficiently weak coupling, quantum chaos, and thus, thermalization is absent. In fact, it is shown that the critical disorder, at which the metal-insulator transition of its environment occurs in the absence of the central degree of freedom, is modified by the coupling strength of the central degree of freedom. To demonstrate this, a phase diagram is derived. Within the localized phase, logarithmic growth of entanglement entropy, a typical signature of many-body localized systems, is increased by the coupling to the central spin. This property is traced back to resonantly coupling spins within the localized Heisenberg chain and analytically derived in the absence of interactions. Thus, the studied model of free fermions is the first model without interactions that mimics the logarithmic spreading of entanglement entropy known from many-body localized systems. Eventually, it is demonstrated that observables regarding the central spin significantly break the eigenstate thermalization hypothesis within the localized phase. Therefore, it is demonstrated how a central spin can be employed as a detector of many-body localization.},
  subject      = {Quanteninformatik},
  language  = {en}
}