| Abstract: | I will present an overview of some recent results on many-body localization and thermalization in interacting isolated quantum systems in the presence of disorder. Such systems thermalize if the disorder is sufficiently weak and satisfy the eigenstate thermalization hypothesis (ETH), which predicts a special structure of local operators in the eigenbasis of the Hamiltonian. At strong disorder, ETH is violated and particles are localized, preventing thermalization. The transition between the thermalizing and the many-body localized regimes can be understood as an eigenstate phase transition, where the local structure of eigenstates of the Hamiltonian changes drastically, as reflected for example in the
entanglement properties. |