Abstract of Ephraim Bernhardt's thesis

Abstract:

This PhD thesis is concerned with the interplay of effects of disorder, localization, interaction with the environment and topology in quantum many-body systems. It aims at studying this interface both from a fundamental interest, as well as to develop perspectives with regards to applications in quantum technology. A special focus of this thesis is on spin systems, as they form a convenient platform for probing above mentioned effects and are also interesting from the perspective of experimental realizations and applications. Starting from a single spin-1/2 in a radial magnetic field, topology can be defined from the poles of the ground state manifold. This model is analogous to several other condensed matter models, such as the Haldane model or the Kitaev wire. The definition of topology in the spin model can be extended to interacting systems composed of several spins and for open systems coupled to an environment. Experimentally, this topology can be probed from a dynamic protocol driving the magnetic field acting on the spin in time. For this setup, the thesis investigates a ‘quantum dynamo effect’ occurring as a consequence of the driven dissipative dynamics when coupling to an environment. There is a curious relation of this effect with the 'dynamically accessed topology’ of the spin. This thesis investigates and defines thermodynamic properties of this effect corresponding to a work-to-work conversion coherently displacing certain modes of the environment and thus opening perspectives for energy transfer on the nanoscale through an environment when coupling several systems to a common bath. The definitions and probes are compared using different analytical and numerical techniques for evaluating the driven dissipative dynamics. In interacting systems composed of several spins, the topology of each spin can be studied and has previously been shown to yield fractional values depending on the symmetry of the model. This thesis emphasizes the behavior of this fractional topological phase upon introduction of disorder and shows that the latter can lead to its extension. An interpretation of these effects in terms of Majorana fermions is discussed and allows to think about applications for quantum information. The effects of disorder and localization physics are discussed in depth for a model which can be realized from cold atoms and can in a certain limit be mapped to a spin model as well. A particular form of quenched disorder can be realized in this system through coupling to a second particle species. In this case, there is an interesting connection to Z2 lattice gauge theories when the impurities introducing disorder to the system acquire a quantum dynamics themselves. This thesis studies the interplay of an applied U(1) gauge field allowing to define a local current with this special form of disorder and in particular proposes to use this current as an indicator of the localization properties. A numerical study using exact diagonalisation demonstrates the presence of a many-body localized phase in this model. It is identified from the scaling of the entanglement entropy and witnessed by the bipartite fluctuations and the local current. The thesis offers perspectives for a fundamental understanding of the interplay of topology, open system dynamics and disorder effects in quantum systems and bridges with experimental realizations and applications.