Hilbert-space fragmentation, multifractality, and many-body localization
arXiv:1906.05709 · doi:10.1016/j.aop.2021.168502
Abstract
Investigating many-body localization (MBL) using exact numerical methods is limited by the exponentialgrowth of the Hilbert space. However, localized eigenstates display multifractality and only extend over a vanishing fraction of the Hilbert space. Here, building on this remarkable property, we develop a simple yet efficient decimation scheme to discard the irrelevant parts of the Hilbert space of the random-field Heisenberg chain. This leads to an Hilbert space fragmentation in small clusters, allowing to access larger systems at strong disorder. The MBL transition is quantitatively predicted, together with a geometrical interpretation of MBL multifractality as a shattering of the Hilbert space.
arXiv commentSpecial Issue of the Annals of Physics, Localisation 2020, dedicated to Philip W. Anderson
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