有限程晶格模型转移矩阵的异常超曲面及其对量子输运性质的影响
Exceptional hypersurfaces of transfer matrices of finite-range lattice models and their consequences on quantum transport properties
AI总结：
本文研究了有限程一维晶格模型非厄米转移矩阵的异常点，发现带边总是对应异常点且电导在带边处普遍呈现 N^{-2} 亚扩散标度，并证明有限程跃迁可系统生成高阶异常点。
摘要：
我们研究了有限程一维晶格模型非厄米转移矩阵中位于异常超曲面上的异常点的出现及其性质。我们揭示了这些异常点在决定非平衡稳态下电导随系统尺寸标度行为中的非平凡作用。我们观察到系统的带边总是对应于转移矩阵异常点。有趣的是，尽管下带边总是出现在波矢 $k=0$ 处，上带边可能对应也可能不对应于 $k=π$。尽管如此，在所有情况下，系统在每个带边处都表现出普适的亚扩散输运行为，电导按 $N^{-b}$ 标度，标度指数为 $b=2$。然而，当上带边不位于 $k=π$ 时，电导呈现出有趣的振荡，整体仍保持 $N^{-2}$ 标度。我们的工作进一步揭示，当考虑超越最近邻的有限程跃迁时，该体系特别适合在上带边系统地生成高阶转移矩阵异常点。研究表明，除带边之外还存在其他异常点，但有趣的是，这些异常点不会导致反常输运。
英文摘要：
We investigate the emergence and corresponding nature of exceptional points located on exceptional hyper-surfaces of non-hermitian transfer matrices for finite-range one-dimensional lattice models. We unravel the non-trivial role of these exceptional points in determining the system size scaling of electrical conductance in non-equilibrium steady state. We observe that the band edges of the system always correspond to the transfer matrix exceptional points. Interestingly, albeit the lower band edge always occurs at wave-vector $k=0$, the upper band edge may or may not correspond to $k=π$. Nonetheless, in all the cases, the system exhibits universal subdiffusive transport for conductance at every band edge with scaling $N^{-b}$ with scaling exponent $b= 2$. However, for cases when the upper band edge is not located at $k=π$, the conductance features interesting oscillations with overall $N^{-2}$ scaling. Our work further reveals that this setup is uniquely suited to systematically generate higher order transfer matrix exceptional points at upper band edge when one considers finite range hoppings beyond nearest neighbour. Additional exceptional points other than those at band edges are shown to occur, although interestingly, these do not give rise to anomalous transport.
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