The conductance of disordered quantum wires vanishes at any temperature, under very general conditions, if charge carriers do not exchange energy with each other or with their environment. This fundamental phenomenon—known as Anderson localization—was discovered more than 65 years ago. Over the past two decades, the field has experienced a resurgence of interest following arguments that localization can persist even in the presence of interactions, provided they are not too strong: a phenomenon known as many-body localization (MBL). In 2022, the Lars Onsager Prize was awarded for foundational work on MBL, reflecting its fundamental implications for the understanding of thermalization.
 

The talk will present numerical investigations into the effects of short-range interactions in disordered, single-channel quantum wires. The first part offers an overview of the field of MBL, focusing on the dynamical behavior of two key observables: entanglement entropy and sublattice imbalance. The second part highlights a concept in many-body dynamics that we have recently introduced: the “potential-energy surface.” This concept establishes an analogy between the relaxation of a many-body state in Fock space and a previously unexplored variant of a percolation problem. Potential implications for MBL phase diagrams will also be briefly discussed.