  We study the many body localization (MBL) transition for interacting fermions
subject to quasiperiodic potentials by constructing the local integrals of
motion (LIOMs) in the MBL phase as time-averaged local operators. We study
numerically how these time-averaged operators evolve across the MBL transition.
We find that the norm of such time-averaged operators drops discontinuously to
zero across the transition; as we discuss, this implies that LIOMs abruptly
become unstable at some critical localization length of order unity. We analyze
the LIOMs using hydrodynamic projections and isolating the part of the operator
that is associated with interactions. Equipped with this data we perform a
finite-size scaling analysis of the quasiperiodic MBL transition. Our results
suggest that the quasiperiodic MBL transition occurs at considerably stronger
quasiperiodic modulations, and has a larger correlation-length critical
exponent, than previous studies had found.
