Perturbative Study of Local Integrals of Motion and Transport in Weakly Interacting Localized Fermions

Interacting systems that display many-body localization strongly violate the eigenstate thermalization hypothesis. It is believed that localization is preserved in the Anderson model perturbed by interactions, giving rise to a many-body localized phase for finite interaction strengths. We here study the fate of localization using a perturbative approach in the interaction strength. Through large-scale numerical simulations, we study the adiabatic gauge potential (AGP) -- a probe for quantum chaos -- at low orders in perturbation theory. We use the AGP to compute corrections to local integrals of motion (LIOMs). We find that for a finite fraction of the LIOMs the corrections are well-controlled in the leading order, while some LIOMs suffer from local resonances. Additionally, we perturbatively study charge-transporting properties of the particle current operator in this weakly interacting model and find that charge transport is suppressed and bounded to first order.