论文标题
在远程Aubry-André-Harper模型中的离域特征状态的分数
Fraction of delocalized eigenstates in the long-range Aubry-André-Harper model
论文作者
论文摘要
We uncover a systematic structure in the single particle phase-diagram of the quasiperiodic Aubry-André-Harper(AAH) model with power-law hoppings ($\sim \frac{1}{r^σ}$) when the quasiperiodicity parameter is chosen to be a member of the `metallic mean family' of irrational Diophantine numbers.除了完全离界和本地化阶段，我们还发现多次分子（局部）状态与Delabalized States共存，价格为$σ<1 $（$σ> 1 $）。这些阶段中的分离本特征状态的比例可以从一般序列中获得，这是“金属平均家族”的数学特性的表现。如果费米水平属于局部制度，则非互动多体基地状态的纠缠熵尊重该区域法，同时，如果费米级属于Delaparithmi-Level，则违反它。对数违反术语的预成分在不同阶段显示出有趣的行为。纠缠熵也显示了与金属均值有关的特殊填充分数的特殊填充分数中的区域法。
We uncover a systematic structure in the single particle phase-diagram of the quasiperiodic Aubry-André-Harper(AAH) model with power-law hoppings ($\sim \frac{1}{r^σ}$) when the quasiperiodicity parameter is chosen to be a member of the `metallic mean family' of irrational Diophantine numbers. In addition to the fully delocalized and localized phases we find a co-existence of multifractal (localized) states with the delocalized states for $σ<1$ ($σ>1$). The fraction of delocalized eigenstates in these phases can be obtained from a general sequence, which is a manifestation of a mathematical property of the `metallic mean family'. The entanglement entropy of the noninteracting many-body ground states respects the area-law if the Fermi level belongs in the localized regime while logarithmically violating it if the Fermi-level belongs in the delocalized or multifractal regimes. The prefactor of logarithmically violating term shows interesting behavior in different phases. Entanglement entropy shows the area-law even in the delocalized regime for special filling fractions, which are related to the metallic means.
