临界离域量子物质中的Chalker标度、能级排斥和共形不变性：无序拓扑超导体和人造石墨烯
Chalker scaling, level repulsion, and conformal invariance in critically delocalized quantum matter: Disordered topological superconductors and artificial graphene
摘要：
我们数值研究临界离域波函数模型的二维狄拉克费米子，矢量势无序。这些描述了3D拓扑超导体的表面状态，也可以通过分子石墨烯等人造材料中的长程相关键随机性来实现。在这些系统中，对于强无序，可以发生冻结状态，其中单个波函数呈现出由宏观距离分开的几个局部峰。尽管这种稀薄的空间结构，我们发现强大的本征态之间的相关性在不同的能量，在弱和强的混乱。相关的能级统计量总是近似于Wigner-Dyson。该系统显示广义Chalker（量子临界）标度，即使当个别国家是准本地化的空间。我们证实了态密度和多重分形谱的分析预测。对于一个单一的狄拉克谷，我们建立了有限的能量状态显示出普遍的多重分形谱与整数量子霍尔平台过渡一致。因此，一个有限能量的狄拉克费米子可以表现为量子霍尔临界金属。对于双谷和非阿贝尔无序的情形，我们验证了共形场论的预言。我们的结果为非阿贝尔的情况下，意味着离域和共形不变性的拓扑保护的多路拓扑超导体表面状态。
英文摘要：
We numerically investigate critically delocalized wavefunctions in models of 2D Dirac fermions, subject to vector potential disorder. These describe the surface states of 3D topological superconductors, and can also be realized through long-range correlated bond randomness in artificial materials like molecular graphene. A frozen regime can occur for strong disorder in these systems, wherein a single wavefunction presents a few localized peaks separated by macroscopic distances. Despite this rarefied spatial structure, we find robust correlations between eigenstates at different energies, at both weak and strong disorder. The associated level statistics are always approximately Wigner-Dyson. The system shows generalized Chalker (quantum critical) scaling, even when individual states are quasilocalized in space. We confirm analytical predictions for the density of states and multifractal spectra. For a single Dirac valley, we establish that finite energy states show universal multifractal spectra consistent with the integer quantum Hall plateau transition. A single Dirac fermion at finite energy can therefore behave as a Quantum Hall critical metal. For the case of two valleys and non-abelian disorder, we verify predictions of conformal field theory. Our results for the non-abelian case imply that both delocalization and conformal invariance are topologically-protected for multivalley topological superconductor surface states.
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