Scaling of the bulk polarization in extended and localized phases of a quasiperiodic model,Physical Review B

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Scaling of the bulk polarization in extended and localized phases of a quasiperiodic model
Physical Review B ( IF 3.2 ) Pub Date : 2024-09-11 , DOI: 10.1103/physrevb.110.125124
Balázs Hetényi _{1,

2}

Affiliation

We study the finite size scaling of the bulk polarization in a quasiperiodic (Aubry-André) model using the geometric analog of the Binder cumulant. As a proof of concept, we show that the geometric Binder cumulant method described here can reproduce the known literature values for the flat and raised cosine distributions, which are the two distributions that occur in the delocalized phase. For the Aubry-André model at half-filling, the phase transition point is accurately reproduced. Not only is the correct size scaling exponent of the variance obtained in the extended and the localized phases, but the geometric Binder cumulant undergoes a sign change at the phase transition. We also calculate the state resolved Binder cumulant as a function of disorder strength to gain insight into the mechanism of the localization transition.

中文翻译：

准周期模型的扩展相和局域相中体极化的缩放

我们使用 Binder 累积量的几何模拟来研究准周期 (Aubry-André) 模型中体偏振的有限尺寸缩放。作为概念证明，我们表明这里描述的几何 Binder 累积量方法可以重现平坦和升余弦分布的已知文献值，这是发生在离域阶段的两种分布。对于半填充时的 Aubry-André 模型，可以准确地再现相变点。不仅在扩展阶段和局部阶段中获得了正确的方差大小缩放指数，而且几何 Binder 累积量在相变时经历了符号变化。我们还计算了状态解析的 Binder 累积量作为无序强度的函数，以深入了解定位转变的机制。

更新日期：2024-09-11

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