Title: Exploring one particle orbitals in large Many-Body Localized systems,
Abstract: Strong disorder in interacting quantum systems can give rise to the
phenomenon of Many-Body Localization (MBL), which defies thermalization due to
the formation of an extensive number of quasi local integrals of motion. The
one particle operator content of these integrals of motion is related to the
one particle orbitals of the one particle density matrix and shows a strong
signature across the MBL transition as recently pointed out by Bera et al.
[Phys. Rev. Lett. 115, 046603 (2015); Ann. Phys. 529, 1600356 (2017)]. We study
the properties of the one particle orbitals of many-body eigenstates of an MBL
system in one dimension. Using shift-and-invert MPS (SIMPS), a matrix product
state method to target highly excited many-body eigenstates introduced in
[Phys. Rev. Lett. 118, 017201 (2017)], we are able to obtain accurate results
for large systems of sizes up to L = 64. We find that the one particle orbitals
drawn from eigenstates at different energy densities have high overlap and
their occupations are correlated with the energy of the eigenstates. Moreover,
the standard deviation of the inverse participation ratio of these orbitals is
maximal at the nose of the mobility edge. Also, the one particle orbitals 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.