Exploring one particle orbitals in large Many-Body Localized systems

Strong disorder in interacting quantum systems can give rise to Many-Body Localization (MBL), which defies thermalization due to the formation of an extensive number of quasi local integrals of motion. The one particle content of these integrals of motion is related to the one particle orbitals (OPOs) of the one particle density matrix, which shows a strong signature across the transition as pointed out by Bera et al. In this work we study the OPOs of eigenstates of an MBL system.We obtain accurate results for sizes up to L = 64. We find that the OPOs of eigenstates at different energy densities have high overlap and their occupations are correlated with the energy of the eigenstates. Moreover, single MBL eigenstates at the mobility edge present two sets of qualitatively different OPOs, and so they are aware of the presence of an ergodic phase. Also, the OPOs decay exponentially in real space, with a correlation length that increases at low disorder. In addition, we find a 1/f distribution of the coupling constants of a certain range of the number operators of the OPOs, which is related to their exponential decay.