Abstract
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.
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