Hilbert-space fragmentation, multifractality, and many-body localization

Investigating many-body localization (MBL) using exact numerical methods is limited by the exponential growth 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 a 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. (C) 2021 Elsevier Inc. All rights reserved.

Automated summary

Investigating many-body localization is challenging due to the exponential growth of the Hilbert space, but a new method has been developed to efficiently discard irrelevant parts and access larger systems at strong disorder, leading to a quantitative prediction of the MBL transition with a geometric interpretation of the multifractality of the Hilbert space.