Masters Thesis

Many-body localization and mobility edge in spin chain systems with quasiperiodic fields

The study of many-body localization (MBL) helps address questions at the very foundation of quantum statistical mechanics—chiefly, can an isolated quantum system serve as a thermal bath for its own subsystems? We study the many-body localization of spin chain systems with quasiperiodic fields. Based on finite-size scaling analysis of entanglement entropy and fluctuations of the bipartite magnetization, we identify W_c > 1.85 as a lower bound for the critical disorder necessary to drive the MBL phase transition. We also examine the entanglement entropy of an initial product state after a global quantum quench where we find power-law and logarithmic growth for the thermal and many-body localized phases, respectively, with a transition point W_c ~ 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. We also observe the appearance of a mobility edge in small quasiperiodic systems and explore density matrix renormalization group methods to probe larger systems. 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.

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