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DOE OSTI · 23183175

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

Pietracaprina, Francesca·Laflorencie, Nicolas
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Abstract

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.

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71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICSEIGENSTATESFRAGMENTATIONHILBERT SPACEMANY-BODY PROBLEMRANDOMNESS

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Pietracaprina, Francesca, Laflorencie, Nicolas. 2021-12-15. Hilbert-space fragmentation, multifractality, and many-body localization. https://doi.org/10.1016/j.aop.2021.168502

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