Many-body mobility edge due to symmetry-constrained dynamics and strong interactions

Abstract

We provide numerical evidence combined with an analytical understanding of the many-body mobility edge for the strongly anisotropic spin-$1/2 \mathit{XXZ}$ model in a random magnetic field. The system dynamics can be understood in terms of symmetry-constrained excitations about parent states with ferromagnetic and antiferromagnetic short range order. These two regimes yield vastly different dynamics producing an observable, tunable many-body mobility edge. We compute a set of diagnostic quantities that verify the presence of the mobility edge and discuss how weakly correlated disorder can tune the mobility edge further.