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

Francesca Pietracaprina; Nicolas Laflorencie

doi:10.1016/j.aop.2021.168502

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arXiv · 1906.05709

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

Francesca Pietracaprina·Nicolas Laflorencie

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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.

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BibTeX RIS

Francesca Pietracaprina, Nicolas Laflorencie. 2021-04-19. Hilbert-space fragmentation, multifractality, and many-body localization. https://doi.org/10.1016/j.aop.2021.168502

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