Interaction-Induced Characteristic Length in Strongly Many-Body Localized Systems

We propose a numerical method for explicitly constructing a complete set of local integrals of motion (LIOM) and definitely show the existence of LIOM for strongly many-body localized systems. The method combines exact diagonalization and nonlinear minimization, and gradually deforms the LIOM for the noninteracting case to those for the interacting case. By using this method we find that for strongly disordered and weakly interacting systems, there are two characteristic lengths in the LIOM. The first one is governed by disorder and is of Anderson-localization nature. The second one is induced by interaction but shows a discontinuity at zero interaction, showing a nonperturbative nature. We prove that the entanglement and correlation in any eigenstate extend not longer than twice the second length and thus the eigenstates of the system are `quasi-product states' with such a localization length.