Quantum quenches in the many-body localized phase

Maksym Serbyn, Zlatko Papić, Dmitry A. Abanin

Many-body localized (MBL) systems are characterized by the absence of transport and thermalization and, therefore, cannot be described by conventional statistical mechanics. In this paper, using analytic arguments and numerical simulations, we study the behavior of local observables in an isolated MBL system following a quantum quench. For the case of a global quench, we find that the local observables reach stationary, highly nonthermal values at long times as a result of slow dephasing characteristic of the MBL phase. These stationary values retain the local memory of the initial state due to the existence of local integrals of motion in the MBL phase. The temporal fluctuations around stationary values exhibit universal power-law decay in time, with an exponent set by the localization length and the diagonal entropy of the initial state. Such a power-law decay holds for any local observable and is related to the logarithmic in time growth of entanglement in the MBL phase. This behavior distinguishes the MBL phase from both the Anderson insulator (where no stationary state is reached) and from the ergodic phase (where relaxation is expected to be exponential). For the case of a local quench, we also find a power-law approach of local observables to their stationary values when the system is prepared in a mixed state. Quench protocols considered in this paper can be naturally implemented in systems of ultracold atoms in disordered optical lattices, and the behavior of local observables provides a direct experimental signature of many-body localization.

Julian Léonard, Matthew Rispoli, Alexander Lukin +4 more

Marianna Sorba, Nicolò Defenu, Gesualdo Delfino A

Anirban Dutta, Subroto Mukerjee, K. Sengupta

We chart out the ground state phase diagram and demonstrate the presence of a many-body localized (MBL) phase for an experimentally realizable one-dimensional (1D) constrained dipole boson model in the presence of an Aubry-Andre (AA) potential whose strength ${\ensuremath{\lambda}}_{0}$ can be tuned to precipitate an ergodic-MBL transition. We discuss the signature of such a transition in the quantum dynamics of the model by computing its response subsequent to a sudden quench of ${\ensuremath{\lambda}}_{0}$. We show that the MBL and the ergodic phases can be clearly distinguished by study of post-quench dynamics and provide an estimate for minimal time up to which experiments need to track the response of the system to confirm the onset of the MBL phase. We suggest experiments which can test our theory.

Ravi Kumar, Ranjan Modak

While global quantum quench has been extensively used in the literature to understand the localization-delocalization transition for the one-dimensional quantum spin chain, the effect of geometric quench (which corresponds to a sudden change of the geometry of the chain) in the context of such transitions is yet to be well understood. In this work, we investigate the effect of geometric quench in the Aubry-Andr\'e model, which supports localization-delocalization transition even in one dimension. We study the spreading of the entanglement and the site occupation with time and find many interesting features that can be used to characterize localization-delocalization transition. We observe that geometric quench causes a power-law type growth of the entanglement entropy in the delocalized phase in contrast to the linear growth which is found in the global quench studies. We also find that the saturation values in the many-body localized (MBL) phase obey area law in contrast to the usual volume law, which is a signature feature of the MBL phase in the context of global quench. This area law can also be understood from the long time site-occupation profile in the MBL phase.

Sorba, Marianna, Nicolò Defenu, Delfino, Gesualdo