# *Special* HET Seminar: "Many-body Localization: Breakdown of Thermalization in Quantum Matter"

Until recently interacting many-particle systems governed by the laws of quantum mechanics were assumed to eventually reach thermal equilibrium, being described by equilibrium statistical physics. Rapid developments in theory and experiments in the last decade have established a phase of matter where this assumption is false, due to a phenomenon known as many-body localization (MBL). In this phase, the system undergoing unitary time dynamics retains the memory of the initial state in local observables for infinitely long times. I will give an overview of the theoretical and experimental progress in this growing field at the intersection of condensed matter physics, quantum information science, and atomic physics. I will describe the emergent integrability of the MBL phase which gives rise to area-law entanglement for the full many-body spectrum of eigenstates. This structure of the eigenstates allows for an efficient description of the system using shallow quantum circuits. MBL also gives rise to novel forms of quantum phase transitions even in states at finite energy densities. I will conclude with some of the open questions in this field.