论文标题
非富米系统中受对称保护的特殊和淋巴结点
Symmetry-protected exceptional and nodal points in non-Hermitian systems
论文作者
论文摘要
非热词〜（NH）系统的独特特征之一是被称为特殊点〜（EPS）的非铁毒性变性的外观。当哈密顿量变得不可用时，发生了广泛研究的有缺陷的EPS。除了这种堕落之外，我们还表明，NH系统可能会持有另外两种类型的归化性，即无缺陷的EPS和普通的（Hermitian）淋巴结点。无缺陷的EPS通过i）在这些点上的NH哈密顿量的对角度表现出来，ii）沿这些点和III的某些交叉点，哈密顿量的非双向配分性）在约旦分解中的某些交叉点在某些方向上接近点时的分解。我们证明了某些离散对称性，即平等时代，奇迹颗粒孔和伪 - 温米特对称性，可以保证出现有缺陷和非缺陷的EPS。我们通过在两个波段系统中包括NH时间反转对称性来扩展此对称性列表。两频和四波段模型体现了我们的发现。通过一个示例，我们进一步揭示了普通的节点点在放松上述对称性时可能与NH模型中的EPS存在并存。
One of the unique features of non-Hermitian~(NH) systems is the appearance of non-Hermitian degeneracies known as exceptional points~(EPs). The extensively studied defective EPs occur when the Hamiltonian becomes non-diagonalizable. Aside from this degeneracy, we show that NH systems may host two further types of degeneracies, namely, non-defective EPs and ordinary (Hermitian) nodal points. The non-defective EPs manifest themselves by i) the diagonalizability of the NH Hamiltonian at these points, ii) the non-diagonalizability of the Hamiltonian along certain intersections of these points and iii) instabilities in the Jordan decomposition when approaching the points from certain directions. We demonstrate that certain discrete symmetries, namely parity-time, parity-particle-hole, and pseudo-Hermitian symmetry, guarantee the occurrence of both defective and non-defective EPs. We extend this list of symmetries by including the NH time-reversal symmetry in two-band systems. Two-band and four-band models exemplify our findings. Through an example, we further reveal that ordinary nodal points may coexist with defective EPs in NH models when the above symmetries are relaxed.
