Many-body localization in spin chain systems with quasiperiodic fields

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 Wc>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, with a transition point Wc~2.5. 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 many-body localized phase transition.