SemiLIOM · Semiclassical understanding of ergodicity-breaking in many-body systems

The detailed understanding of quantum many-body effects is a highly relevant task in modern condensed matter physics. It is assumed that quantum many-body systems generically exhibit a notion of ergodicity, captured by the eigenstate thermalization hypothesis. However, it is numerically observed that there exist various ergodicity-breaking effects, which violate this assumption of fundamental thermodynamics. The most prominent example of such ergodicity-breaking is many-body localization (MBL), which arises from an emergent integrability induced by local integrals of motion. Despite the conceptual analytic intuition, most investigations on many-body localization are confined to small-sized numerical studies, only. The project goes beyond this state in devising an analytical view on ergodicity-breaking by combining concepts from many-body physics with modern classical and semiclassical techniques. The aim of this project is to rigorously transfer the notion of classical integrability by means of the Kolmogorov-Arnold-Moser (KAM) theory towards the emergent integrability of MBL in the semiclassical regime. To this end, the study provides a detailed understanding of the transition from MBL to ergodicity, and thereby lays out the foundations for a many-body KAM theory in terms of symplectic geometry. Furthermore, as entanglement is the central observable of ergodicity-breaking, the project is complemented with an analytical investigation of entanglement in the semiclassical regime. The current advances in the experimental realization of quantum simulators and quantum computers render this project to be highly relevant and timely. The completion of the project will provide the missing link between classical KAM theory and quantum mechanics and establishes a firm foundation for future investigations of the quantum-classical correspondence in many-body systems.