Emergent quasicrystals in strongly correlated systems
Emergent quasicrystals in strongly correlated systems
复制标题
强相关系统中出现的准晶体
DOI：
10.1103/physrevb.94.035131
复制
发表时间：
2015
影响因子：
3.7
通讯作者：
Z. Nussinov
中科院分区：
文献类型：
--
作者：
E. Sagi;Z. Nussinov
在许多强相互作用的电子系统中，可公度性是至关重要的。在分数量子霍尔效应中，在较大的分母填充分数处出现越来越窄的高原的丰富级联。在高温超导体和其他电子系统中，在某些填充分数下也会出现丰富的相称结构。一个自然的问题涉及这些和其他电子系统在不合理的填充分数的字符。在这里，我们表明，准晶结构自然出现在这些情况下，并触发行为通常不预期的周期性系统。我们首先证明了非理性填充量子霍尔系统在薄环面极限下可以过渡到准周期有序结构。利用准晶体的已知性质，我们认为，这些国家是不稳定的对无序的影响，与量子霍尔高原的存在。然后，我们研究类似的物理情况下，在一个系统的冷里德伯原子放置在一个光学晶格。这样的实验装置通常是无无序的，因此可以用来检测我们预测的涌现准晶体。我们讨论了类似的情况下，Falicov-Kimball模型，已知的精确结果可以用来建立准晶结构在一个和两个维度。我们简要地推测我们的理论研究结果和存在的玻璃动力学和其他功能的强相关的电子系统之间的可能关系。
Commensurability is of paramount importance in numerous strongly interacting electronic systems. In the Fractional Quantum Hall effect, a rich cascade of increasingly narrow plateaux appear at larger denominator filling fractions. Rich commensurate structures also emerge, at certain filling fractions, in high temperature superconductors and other electronic systems. A natural question concerns the character of these and other electronic systems at irrational filling fractions. Here we demonstrate that quasicrystalline structures naturally emerge in these situations, and trigger behaviors not typically expected of periodic systems. We first show that irrationally filled quantum Hall systems cross over into quasiperiodically ordered configuration in the thin-torus limit. Using known properties of quasicrystals, we argue that these states are unstable against the effects of disorder, in agreement with the existence of quantum Hall plateaux. We then study analogous physical situations in a system of cold Rydberg atoms placed on an optical lattice. Such an experimental setup is generally disorder free, and can therefore be used to detect the emergent quasicrystals we predict. We discuss similar situations in the Falicov-Kimball model, where known exact results can be used to establish quasicrystalline structures in one and two dimensions. We briefly speculate on possible relations between our theoretical findings and the existence of glassy dynamics and other features of strongly correlated electronic systems.