Journal
ANNALS OF PHYSICS
Volume 435, Issue -, Pages -Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.aop.2021.168502
Keywords
Many-body localization; Exact diagonalization; Multifractality
Categories
Funding
- French National Research Agency (ANR) [THERMOLOC ANR16-CE30-0023-02]
- CALMIP, France [2017-P0677, 2018-P0677]
- GENCI, France [x2018050225]
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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.
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.
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