标题： 幂律衰减本征态中的涌现多分形性 显示英文标题

标题： Emergent multifractality in power-law decaying eigenstates

摘要： 本征态多分形在量子物理的各个领域具有重要的研究价值并可能有广泛的应用。 以往的大多数研究都集中在精心调节的量子模型上，以实现通常被认为是一种临界现象且对随机扰动非常敏感的多分形性。 在本工作中，我们提出了一组基于本征态幂律衰减的通用原则，使我们能够区分分形相和真正的多分形相。 我们在一种具有非均匀最近邻跃迁的一维紧束缚模型中展示了上述原则，该模型可以通过能量-坐标对偶性映射到标准量子简谐振子。 我们解析计算了分形维数和分形维数谱，结果与数值模拟一致。 显示英文摘要

摘要： Eigenstate multifractality is of significant interest with potential applications in various fields of quantum physics. Most of the previous studies concentrated on fine-tuned quantum models to realize multifractality which is generally believed to be a critical phenomenon and fragile to random perturbations. In this work, we propose a set of generic principles based on the power-law decay of the eigenstates which allow us to distinguish a fractal phase from a genuine multifractal phase. We demonstrate the above principles in a 1d tight-binding model with inhomogeneous nearest-neighbor hopping that can be mapped to the standard quantum harmonic oscillator via energy-coordinate duality. We analytically calculate the fractal dimensions and the spectrum of fractal dimensions which are in agreement with numerical simulations.