超均匀密度分布之间的量子相变
Quantum phase transition between hyperuniform density distributions
摘要：
我们从超均匀性的角度研究了准周期势下的电子分布，旨在建立一种非周期但有序的密度分布的分类和分析方法，准晶体使用Aubry-Andre-Harper模型，我们首先揭示了电子电荷分布的变化，其性质的增加准周期电位改变本征态从扩展到本地化的。虽然这些电荷分布的变化既不具有多重分形特征，也不具有对称性破缺特征，但它们具有超均匀性类及其序度量的特征。我们发现在费米能级，电荷分布直方图，和超均匀性类的状态密度之间的非平凡的关系。除了电子-空穴对称点之外，到不同的超均匀性类的变化作为一阶相变发生，其中该转变是三阶的。此外，我们推广的超均匀度阶度量的函数，捕捉更详细的功能的密度分布，在某种程度上类似于一个推广的分形维数的多重分形。
英文摘要：
We study an electron distribution under a quasiperiodic potential in light of hyperuniformity, aiming to establish a classification and analysis method for aperiodic but orderly density distributions realized in, e.g., quasicrystals. Using the Aubry-Andre-Harper model, we first reveal that the electron-charge distribution changes its character as the increased quasiperiodic potential alters the eigenstates from extended to localized ones. While these changes of the charge distribution are characterized by neither multifractality nor translational-symmetry breaking, they are characterized by hyperuniformity class and its order metric. We find a nontrivial relationship between the density of states at the Fermi level, a charge-distribution histogram, and the hyperuniformity class. The change to a different hyperuniformity class occurs as a first-order phase transition except for an electron-hole symmetric point, where the transition is of the third order. Moreover, we generalize the hyperuniformity order metric to a function, to capture more detailed features of the density distribution, in some analogy with a generalization of the fractal dimension to a multifractal one.
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