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

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 dev...

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Bibliographic Details
Published in:arXiv.org 2021-04
Main Authors: Pietracaprina, Francesca, Laflorencie, Nicolas
Format: Article
Language:English
Subjects:
Eigenvectors
Fragmentation
Hilbert space
Localization
Many body interactions
Numerical methods
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1906.05709