Large-Scale Structure of Entanglement

forthcoming

Entanglement is the key resource for quantum information processing. Its study has revolutionized our understanding of condensed matter, quantum fields and even quantum gravity. One of the most fascinating insights is the connection between the classification of topological phases of matter and long-range entanglement. This project will explore a novel aspect of entanglement in ground states of quantum many-body systems: their large-scale structure of entanglement (LSSE), describing those entanglement properties that are stable against perturbations on arbitrary finite subsystems. Just as macroscopic bulk properties, the large-scale structure of entanglement only sharply reveals itself in systems with an unbounded number of degrees of freedom. Yet, it can uncover entanglement properties of finite-size ground states otherwise invisible, such as their capacity to embezzle entanglement: the task of extracting entanglement without leaving a trace. Relativistic quantum fields and certain critical systems exhibit this counterintuitive property. Remarkably little is known about the LSSE of quantum many-body system and its relation to phases of matter. Moreover, the LSSE of quantum fields has been argued to be radically modified by gravity -- disabling their ability to embezzle entanglement. Holographic duality in turn establishes a correspondence between quantum gravity and critical many-body systems, placing the LSSE at the center of modern theoretical physics. The project LargEnt will establish a new paradigm to describe the entanglement content of many-body systems, by a) developing the necessary tools to determine the LSSE, b) clarifying the relation between LSSE, criticality, and topological order, and c) developing a theory to determine whether ground states of many-body systems or vacua of quantum fields can act as multipartite embezzlers. The results of LargEnt will add a new dimension to the classification of ground states of many-body systems.