Finite-size effects have been a major and justifiable source of concern for studies of many-body localization, and several works have been dedicated to the subject. In this Letter, however, we discuss yet another crucial problem that has received much less attention, that of the lack of self-averaging and the consequent danger of reducing the number of random realizations as the system size increases. By taking this into account and considering ensembles with a large number of samples for all system sizes analyzed, we find that the generalized dimensions of the eigenstates of the disordered Heisenberg spin-1/2 chain close to the transition point to localization are described remarkably well by an exact analytical expression derived for the noninteracting Fibonacci lattice, thus providing an additional tool for studies of many-body localization.

中文翻译：

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多体定位转换中的多重分形和自平均

有限尺寸效应一直是多体定位研究的主要和合理的关注来源，并且有几项工作致力于该主题。然而，在这封信中，我们讨论了另一个很少受到关注的关键问题，即缺乏自我平均以及随着系统规模增加而减少随机实现数量的风险。通过考虑到这一点并考虑对所有系统规模分析的具有大量样本的集合，我们发现无序海森堡自旋 1/2 链的本征态的广义维数被描述得非常好。通过为非相互作用的斐波那契晶格导出的精确解析表达式，从而为多体定位研究提供了额外的工具。