Motivated by the findings of logarithmic spreading of entanglement in a many-body localized system, we identify and untangle two factors contributing to the spreading of entanglement in the fully many-body localized phase, where all many-body eigenstates are localized. Performing full diagonalizations of an $XXZ$ spin model with random longitudinal fields, we demonstrate a linear dependence of the spreading rate on the decay length $(\ensuremath{\xi})$ of the effective interaction between localized pseudospins (l-bits), which depends on the disorder strength, and on the final value of entanglement per spin $({s}_{\ensuremath{\infty}})$, which primarily depends on the initial state. The entanglement entropy thus grows with time as $\ensuremath{\sim}\ensuremath{\xi}\ifmmode\times\else\texttimes\fi{}{s}_{\ensuremath{\infty}}logt$, providing support for the phenomenology of many-body localized systems proposed by Huse and Oganesyan.Motivated by the findings of logarithmic spreading of entanglement in a many-body localized system, we identify and untangle two factors contributing to the spreading of entanglement in the fully many-body localized phase, where all many-body eigenstates are localized. Performing full diagonalizations of an $XXZ$ spin model with random longitudinal fields, we demonstrate a linear dependence of the spreading rate on the decay length $(\ensuremath{\xi})$ of the effective interaction between localized pseudospins (l-bits), which depends on the disorder strength, and on the final value of entanglement per spin $({s}_{\ensuremath{\infty}})$, which primarily depends on the initial state. The entanglement entropy thus grows with time as $\ensuremath{\sim}\ensuremath{\xi}\ifmmode\times\else\texttimes\fi{}{s}_{\ensuremath{\infty}}logt$, providing support for the phenomenology of many-body localized systems proposed by Huse and Oganesyan.

arXiv:1404.5216Physical Review BAug 14, 2014118 citations

Propagation of entanglement in one-dimensional models of many-body localization

Jens Hjorleifur Bardarson, Frank Pollmann, Joel E. Moore

Bulletin of the American Physical SocietyFeb 27, 20120 citations

Geometric quenches in quasidisordered lattice systems

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.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.

arXiv:2201.06813Physical review. B./Physical review. BJun 9, 20221 citation

Storage and transmission of entanglement in a spin chain

Francesco Plastina, Tony J. G. Apollaro, Alexander I. Lvovsky

AIP conference proceedingsJan 1, 20090 citations

XXZ

spin model with random longitudinal fields, we demonstrate a linear dependence of the spreading rate on the decay length $(\ensuremath{\xi})$ of the effective interaction between localized pseudospins (l-bits), which depends on the disorder strength, and on the final value of entanglement per spin $({s}_{\ensuremath{\infty}})$, which primarily depends on the initial state. The entanglement entropy thus grows with time as $\ensuremath{\sim}\ensuremath{\xi}\ifmmode\times\else\texttimes\fi{}{s}_{\ensuremath{\infty}}logt$, providing support for the phenomenology of many-body localized systems proposed by Huse and Oganesyan.