论文标题
具有随机跳跃术语的非热su-schrieffer-Heeger模型的特征值的统计特性
Statistical properties of eigenvalues of the non-Hermitian Su-Schrieffer-Heeger model with random hopping terms
论文作者
论文摘要
我们探讨了Su-Schrieffer-Heeger模型的非富米版本的特征值统计，具有虚构的现场电位和随机分布的跳跃术语。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，特征值也可以纯粹是真实的。事实证明，在这种情况下，在这种情况下，级别的统计数据是高斯正交集合的级别。这表明了一个一般特征，我们澄清说，一个非温和的哈密顿人的特征值纯粹是真实的，可以映射到继承原始哈密顿人的对称性的Hermitian Hamiltonian。当频谱包含虚构特征值时，我们表明状态（DOS）的密度在原点上消失，并且在虚拟轴上的光谱边缘差异。我们表明，DOS的差异源于手性对称的一维遗传系统中的Dyson奇异性，并在分析中得出了DOS的渐近线，这与遗产系统中的渐近性不同。
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.
