Statistical properties of eigenvalues of the non-Hermitian Su-Schrieffer-Heeger model with random hopping terms.,Physical Review E

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Statistical properties of eigenvalues of the non-Hermitian Su-Schrieffer-Heeger model with random hopping terms.
Physical Review E ( IF 2.2 ) Pub Date : 2020-07-01 , DOI: 10.1103/physreve.102.012101
Ken Mochizuki ₁ , Naomichi Hatano ₂ , Joshua Feinberg ₃ , Hideaki Obuse _{1,

2}

Affiliation

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.

中文翻译：

具有随机跳变项的非Hermitian Su-Schrieffer-Heeger模型的特征值的统计特性。

我们探索具有假想的现场势和随机分布的跳变项的非Hermitian版本的Su-Schrieffer-Heeger模型的特征值统计。我们发现，由于哈密顿量的结构，即使在没有奇偶校验和时间反转对称性的情况下，特征值在一定范围的参数中也可以是纯实数。事实证明，在纯实谱的情况下，电平统计是高斯正交系的统计。这表明了一个一般特征，我们可以澄清其特征值是纯实的非埃尔米特哈密顿量可以映射到继承原始哈密顿量对称性的埃尔米特哈密顿量。当频谱包含虚构特征值时，我们表明，状态密度（DOS）在原点消失，而在虚轴上的光谱边缘发散。我们表明，DOS的发散源于手性对称的一维Hermitian系统中的Dyson奇异性，并且从分析上推导了与Hermitian系统中不同的DOS渐近线。

更新日期：2020-07-01

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