Non monotonic influence of Hubbard interaction on the Anderson localization of two-electron wavepackets

We show that the Hubbard-like interaction between two electrons moving in a random one-dimensional potential landscape has a non monotonic influence on the Anderson localization phenomenon. Within a tight-binding approach, we follow the time-evolution of initially localized two-electron wavepackets and compute the participation number of all two-particle eigenstates. We evidence that the coupling between bounded and unbounded two-particle states leads to an overall weakening of Anderson localization of the predominant unbounded states. However, such coupling becomes ineffective in the regime of large interaction strengths on which the energy bands corresponding to these two classes of eigenstates become quite detached. We unveil that these two competing effects are at the origin of the non monotonic influence of the inter-particle interaction on Anderson localization.