具有随机跃迁项的非厄米 Su-Schrieffer-Heeger 模型本征值的统计性质
Statistical properties of eigenvalues of the non-Hermitian Su-Schrieffer-Heeger model with random hopping terms
AI总结：
本文研究含虚在位势与随机跃迁的非厄米 SSH 模型，揭示实谱对应 GOE 统计、复谱虚轴边缘 DOS 呈 Dyson 型发散并给出渐近公式。
摘要：
我们研究了 Su-Schrieffer-Heeger 模型的一种非厄米版本的本征值统计，该模型具有虚在位势和随机分布的跃迁项。我们发现，由于哈密顿量的结构，即使在缺乏宇称和时间反演对称性的情况下，在某一参数范围内本征值也可以完全为实数。结果表明，在这种谱完全为实数的情形中，能级统计属于 Gaussian orthogonal ensemble（高斯正交系综）。这展示了我们所阐明的一个一般特征：本征值完全为实数的非厄米哈密顿量可以映射为一个厄米哈密顿量，而后者继承原哈密顿量的对称性。当谱包含虚本征值时，我们证明态密度（DOS）在原点消失，并在虚轴上的谱边缘处发散。我们证明 DOS 的这种发散源于手性对称的一维厄米系统中的 Dyson 奇点，并解析推导了 DOS 的渐近线，其与厄米系统中的渐近线不同。
英文摘要：
We explore the eigenvalue statistics of a non-Hermitian version of the Su-Schrieffer-Heeger model, with imaginary on-site potentials and randomly distributed hopping terms. We find that owing to the structure of the Hamiltonian, eigenvalues can be purely real in a certain range of parameters, even in the absence of parity and time-reversal symmetry. As it turns out, in this case of purely real spectrum, the level statistics is that of the Gaussian orthogonal ensemble. This demonstrates a general feature which we clarify that a non-Hermitian Hamiltonian whose eigenvalues are purely real can be mapped to a Hermitian Hamiltonian which inherits the symmetries of the original Hamiltonian. When the spectrum contains imaginary eigenvalues, we show that the density of states (DOS) vanishes at the origin and diverges at the spectral edges on the imaginary axis. We show that the divergence of the DOS originates from the Dyson singularity in chiral-symmetric one-dimensional Hermitian systems and derive analytically the asymptotes of the DOS which is different from that in Hermitian systems.
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