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 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.

使用精确数值方法研究多体定位（MBL）受希尔伯特空间指数增长的限制。但是，局部本征态显示出多重分形，并且仅在希尔伯特空间的消失部分上延伸。在此基础上，我们基于此显着特性，开发了一种简单而有效的抽取方案，以丢弃随机场Heisenberg链的希尔伯特空间的无关部分。这导致小集群中的希尔伯特空间碎片化，从而可以在无序情况下访问较大的系统。可以对MBL过渡进行定量预测，并将MBL多重分形的几何解释解释为希尔伯特空间的破裂。