  Local integrals of motion play a central role in the understanding of
many-body localization in many-body quantum systems in one dimension subject to
a random external potential, but the question of how these local integrals of
motion change in a deterministic quasiperiodic potential is one that has
received significantly less attention. Here we develop a powerful new
implementation of the continuous unitary transform formalism and use this
method to directly compute both the effective Hamiltonian and the local
integrals of motion for many-body quantum systems subject to a quasiperiodic
potential. We show that the effective interactions between local integrals of
motion retain a strong fingerprint of the underlying quasiperiodic potential,
exhibiting sharp features at distances associated with the incommensurate
wavelength used to generate the potential. Furthermore, the local integrals of
motion themselves may be expressed in terms of an operator expansion which
allows us to estimate the critical strength of quasiperiodic potential required
to lead to a localization/delocalization transition, by means of a finite size
scaling analysis.
