标题： 通过可观测量界定多重分形性 显示英文标题

标题： Bounding multifractality by observables

摘要： 分形维数已被用作量子多体系统本征态结构的定量度量，对于与随机矩阵理论预测进行比较或区分多体局域系统和混沌系统很有用。 对于能谱中间的混沌系统，态预期为“遍历性”的无限温度态，在热力学极限下所有分形维数趋近于1。 然而，当远离能谱中间时，态会发展出结构，因为它们预期遵循本征态热化假说，少数体可观测量由有限温度系综预测。 我们讨论这种可观测量的结构如何用于从上方限制分形维数，从而解释它们在能量谱上的典型弧形。 然后我们考虑这种上界如何作为多体局域化相变中分形维数的代理，从而正式连接文献中讨论的单粒子和福克空间图像。 显示英文摘要

摘要： Fractal dimensions have been used as a quantitative measure for structure of eigenstates of quantum many-body systems, useful for comparison to random matrix theory predictions or to distinguish many-body localized systems from chaotic ones. For chaotic systems at midspectrum the states are expected to be ``ergodic'', infinite temperature states with all fractal dimensions approaching 1 in the thermodynamic limit. However, when moving away from midspectrum, the states develop structure, as they are expected to follow the eigenstate thermalization hypothesis, with few-body observables predicted by a finite-temperature ensemble. We discuss how this structure of the observables can be used to bound the fractal dimensions from above, thus explaining their typical arc-shape over the energy spectrum. We then consider how such upper bounds act as a proxy for the fractal dimension over the many-body localization transition, thus formally connecting the single-particle and Fock space pictures discussed in the literature.