Mixed spectra and partially extended states in a two-dimensional quasiperiodic model
Mixed spectra and partially extended states in a two-dimensional quasiperiodic model
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DOI：
10.1103/physrevb.101.014205
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发表时间：
2019-09
影响因子：
3.7
通讯作者：
A. Szab'o;U. Schneider
中科院分区：
文献类型：
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作者：
A. Szab'o;U. Schneider
我们介绍了准周期Aubry-Andre模型的二维推广。尽管这个模型表现出与一维模型相同的对偶关系，但它的局部化性质被发现要复杂得多。特别是，对于任意强的准周期调制，出现了部分扩展的单粒子态。它们集中在一个由低无序格线组成的网络上，而格子的其余部分则拥有局域态。这种空间分离保护了局域态不受离域的影响，因此光谱中不会出现迁移率边缘。取而代之的是，局域和部分扩展的状态被穿插，产生了一种不寻常的混合光谱类型，并使复杂的动力学即使在没有相互作用的情况下也能实现。一个明显的例子是，在系统的其余部分仍处于局部状态时，通过低无序线的弹道运输。这种行为对无序和其他微弱的扰动是健壮的。因此，我们的模型直接服从于实验研究，并有望获得引人入胜的多体局部化特性。
We introduce a two-dimensional generalisation of the quasiperiodic Aubry-Andre model. Even though this model exhibits the same duality relation as the one-dimensional version, its localisation properties are found to be substantially more complex. In particular, partially extended single-particle states appear for arbitrarily strong quasiperiodic modulation. They are concentrated on a network of low-disorder lattice lines, while the rest of the lattice hosts localised states. This spatial separation protects the localised states from delocalisation, so no mobility edge emerges in the spectrum. Instead, localised and partially extended states are interspersed, giving rise to an unusual type of mixed spectrum and enabling complex dynamics even in the absence of interactions. A striking example is ballistic transport across the low-disorder lines while the rest of the system remains localised. This behaviour is robust against disorder and other weak perturbations. Our model is thus directly amenable to experimental studies and promises fascinating many-body localisation properties.