  We numerically investigate 1D Bose-Hubbard chains with onsite disorder by
means of exact diagonalization. A primary focus of our work is on
characterizing Fock-space localization in this model from the single-particle
perspective. For this purpose, we compute the one-particle density matrix
(OPDM) in many-body eigenstates. We show that the natural orbitals (the
eigenstates of the OPDM) are extended in the ergodic phase and real-space
localized when one enters into the MBL phase. Furthermore, the distributions of
occupations of the natural orbitals can be used as measures of Fock-space
localization in the respective basis. Consistent with previous studies, we
observe signatures of a transition from the ergodic to the many-body localized
(MBL) regime when increasing the disorder strength. We further demonstrate that
Fock-space localization, albeit weaker, is also evidently present in the
distribution of the physical densities in the MBL regime, both for soft- and
hardcore bosons. Moreover, the full distribution of the densities of the
physical particles provides a one-particle measure for the detection of the
ergodic-MBL transition which could be directly accessed in experiments with
ultra-cold gases.
