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The presence of disorder in a non-interacting system can
localize all energy eigenstates, a phenomena dubbed Anderson
localization. Many-body localization (MBL) is an extension of this
phenomena to include interactions. Effects of interactions show up in
the logarithmic growth of entanglement after a global quench. We
perform a systematic study of the evolution and saturation of
entanglement, and show that it can be used to detect the localization
transition. We consider the bipartite fluctuation which also captures
the transition and is promising as an experimental probe. For
long-range models we find an interesting regime in the non-interacting
disordered chain where the long-time entanglement entropy also shows a
logarithmic growth and the saturated entanglement entropy scales
logarithmically with system size. We further study the interplay of
long-range hopping and interactions on the growth of entanglement and
the MBL transition in this system. We develop an analogy to
higher-dimensional short-range systems to compare and contrast such
behavior with the physics of MBL in a higher dimension.
References:
[1] R. Singh, J. H. Bardarson, and F. Pollmann, “Signatures of the
many-body localization transition in the dynamics of entanglement and
bipartite fluctuations,” New J. Phys., 18, 23046, 2016.
[2] R. Singh, R. Moessner, and D. Roy, “Effect of long-range hopping
and interactions on entanglement dynamics and many-body localization,”
Phys. Rev. B, 95, 94205, 2017.
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