Recent experimental breakthroughs led to realization of tunable, synthetic quantum systems that allow one to probe and manipulate highly non-equilibrium quantum matter. Driving a system ouf-of-equilibrium changes its properties in unexpected ways, opening opportunities for realizing new states of matter. The central goal of this project is to develop a fundamental theoretical understanding of non-equilibrium dynamics and highly excited eigenstates in quantum many-body systems. The conventional wisdom tells that a non-equilibrium system thermalizes, and can then be described by statistical-mechanics. However, recent breakthroughs revealed an experimentally relevant class of systems, the prime example being disordered, many-body localized (MBL) systems, which defy this wisdom, avoiding thermalization. Ergodicity-breaking systems open new avenues for protecting quantum coherence, and for realizing new non-equilibrium phases of matter. We will study the fundamental mechanisms of ergodicity breaking using a multi-disciplinary approach, which builds on techniques from quantum information, condensed matter physics, quantum optics and mathematical physics. We aim to establish universality classes of quantum dynamics, by studying disordered systems with symmetries, and by characterizing entirely new mechanisms of ergodicity breaking, such as quantum many-body scars. In order to overcome the exponential growth of the many-body Hilbert space, new efficient renormalization and tensor-network methods based on quantum entanglement will be developed. Finally, approaches for manipulating quantum matter and realizing new non-equilibrium phases in ongoing experiments will be developed. The completion of this project will lead to a universal theoretical framework for non-equilibrium quantum dynamics, complementing statistical-mechanics in ergodic systems. Such a framework will enable engineering quantum-coherent many-body states with novel properties and functionalities.
