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

Understand

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.