Many-body localization (MBL), the disorder-induced localization of interacting particles, signals a breakdown of conventional thermodynamics because MBL systems do not thermalize and show nonergodic time evolution. We experimentally observed this nonergodic evolution for interacting fermions in a one-dimensional quasirandom optical lattice and identified the MBL transition through the relaxation dynamics of an initially prepared charge density wave. For sufficiently weak disorder, the time evolution appears ergodic and thermalizing, erasing all initial ordering, whereas above a critical disorder strength, a substantial portion of the initial ordering persists. The critical disorder value shows a distinctive dependence on the interaction strength, which is in agreement with numerical simulations. Our experiment paves the way to further detailed studies of MBL, such as in noncorrelated disorder or higher dimensions.We acknowledge financial support by the Deutsche Forschungsgemeinschaft (FOR801, Deutsch-Israelisches Kooperationsprojekt Quantum phases of ultracold atoms in optical lattices), the European Commission (UQUAM and AQuS), the U.S. Defense Advanced Research Projects Agency (Quantum Emulations of New Materials Using Ultracold Atoms), the Minerva Foundation, ISF grant no. 1594/11, Nanosystems Initiative Munich (NIM), and the Swiss Society of Friends of the Weizmann Institute
