Tensor-network analysis of interacting non-reciprocal matter

Thanks to their quantum mechanical nature, interacting microscopic particles can give rise to extraordinary phenomena. Over the last century this led to the discovery of many novel phases of matter such as superconductivity or superfluidity, where particles can move without encountering any resistance. The understanding of these phases and their description has been one of the central topics of modern physics. More recently, innovative experimental platforms with unprecedented control over artificial systems of many quantum particles have become available. Thanks to this new type of experiments, one can simulate interacting quantum-mechanical models, as well as explore new research directions. In particular, these platforms are naturally suited for the study of the physics of systems brought far from their thermal equilibrium. Non-equilibrium systems open a whole new direction in the study of phases of matter, where dynamical properties play a crucial role. An even broader picture emerges when interactions of particles within the system are combined with interactions of the system with its environment. In this setting, one can engineer the coupling to the environment to generate particular properties in the system, that would not be possible otherwise. An intriguing example is given by non-reciprocal systems, where the action- reaction principle is broken and a particle can influence the dynamics of another without being affected by it. During this ESPRIT fellowship, we will study non-reciprocal interacting systems in various settings, with the goal of discovering new phenomena in a growing field of research. This study will be mostly theoretical, and it will utilize advanced numerical techniques to simulate the dynamics of different non-reciprocal systems. We will focus on three main topics. (i) Spreading of entanglement, which represents the building block of quantum information and one of the basic resources for quantum computing. (ii) Transport properties of directional systems, where the non-reciprocal dynamics of particles can lead to the discovery of new behaviors beyond the well-known metallic and insulating ones. (iii) Interplay of topological features and interactions in non-reciprocal systems, and their role in the unique phenomena characterizing these systems. Thanks to the broad range of topics investigated, the result of this project will deepen our understanding of non- reciprocal matter.