Approaching the Many-Body Localization Transition using Matrix Product States: Absence of Griffiths-Type Dynamics in a Thermalizing Quasiperiodic System

During the last decade, a vast body of theoretical work has emerged to characterize the many-body localization (MBL) transition induced by quenched random disorder in 1D lattice models. Nevertheless, all experimental realizations of the MBL transition have relied on quasiperiodic disorder of optical lattices, necessitating a theoretical clarification of the quasiperiodic case. To this end, we employ the “TDVP” matrix product state algorithm of Haegeman et. al. (PRB 2016) to study the relaxation dynamics of local operators in both random and quasiperiodic systems at infinite temperature. In particular, we consider a non-integrable spin chain and approach the MBL transition from the thermal phase by strengthening the disorder. Our preliminary work suggests that the effects of random and quasiperiodic disorder differ. In the random case, we find subdiffusive power law relaxation of the local energy consistent with Griffiths physics. In contrast, the quasiperiodic case exhibits slow, non-power-law relaxation followed by a diffusive power law at late times. This suggests that, despite the initial slow dynamics, genuine Griffiths dynamics are absent in the quasiperiodic system.