  We study the many-body localization of spin chain systems with quasiperiodic
fields. We identify the lower bound for the critical disorder necessary to
drive the transition between the thermal and many-body localized phase to be
$W_{cl}\sim 1.85$, based on finite-size scaling of entanglement entropy and
fluctuations of the bipartite magnetization. We also examine the time evolution
of the entanglement entropy of an initial product state where we find power-law
and logarithmic growth for the thermal and many-body localized phases,
respectively. For larger disorder strength, both imbalance and spin glass order
are preserved at long times, while spin glass order shows dependence on system
size. Quasiperiodic fields have been applied in different experimental systems
and our study finds that such fields are very efficient at driving the MBL
phase transition.
