A macroscopic 'order parameter' for many-body localization
Recent theoretical progress in characterizing many-body localized systems has not been confronted so far with an experimental test. I will present a theoretical analysis of new experimental results showing many-body localization of interacting fermions in a quasi periodic optical lattice potential (arXiv:1501.05661). Specifically we considered the time evolution of a system prepared in a particular many-body initial state, a charge-density wave. Relaxation of the density-wave to a non-vanishing value at long times provides a direct demonstration of the breakdown of ergodicity in the many-body localized state and the saturation value can serve as an order parameter of this state. We found this stationary density wave order to show a distinctive dependence on the interaction strength, in agreement with experiment. Moreover, I will discuss how (temporal) fluctuations in this order parameter are connected to the entanglement-entropy growth, thus providing a distinguishing signature that could be observed in future experiments.