理想平坦陈能带中的量子几何局域化长度与局域化临界性
Quantum geometric localization length and localization criticality in an ideally flat Chern band
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中文总结 AI 辅助
该研究提出理想平坦陈能带的局域化长度由量子几何决定，通过转移矩阵计算发现其存在普适与非普适区域的交叉，为量子霍尔系统局域化及整数量子霍尔跃迁临界性争议提供了新视角。
中文摘要 AI 辅助
我们提出，孤立的理想平坦陈能带中的局域化长度由量子几何决定。我们通过在最大局域化混合Wannier基中应用转移矩阵计算，研究了对应的局域化跃迁及其临界标度，该基的空间展宽可由量子几何长度精确表征。值得注意的是，在调节陈能带的量子度规时，我们观察到从狄拉克不动点控制的普适区域到具有连续变化临界指数的非普适区域的交叉。在普适区域内，局域化长度表现出对量子几何长度的显著线性依赖，这支持了其量子几何本质。这些发现为扭曲莫尔超晶格等量子霍尔系统中的局域化提供了新颖的量子几何视角，并为长期存在的整数量子霍尔跃迁临界性的争议提供了新的思路。
英文摘要
We propose that the localization length in an isolated, ideally flat Chern band is set by quantum geometry. We explore the corresponding localization transition and its critical scaling by applying transfer matrix calculations in the maximally localized hybrid Wannier basis, whose spatial spread is exactly characterized by a quantum geometric length. Remarkably, upon tuning the quantum metric of the Chern band, we observe a crossover from a universal regime controlled by the Dirac fixed point to a non-universal regime with continuously varying critical exponents. Within the universal regime, the localization length exhibits a pronounced linear dependence on the quantum geometric length, supporting its quantum geometric nature. These findings provide a novel quantum geometric perspective on the localization in quantum Hall systems such as twisted moiré superlattices, and shed new light on the long-standing controversy over the criticality of the integer quantum Hall transition.
