Exceptional points (EPs) are spectral defects displayed by non-Hermitian systems in which multiple degenerate eigenvalues share a single eigenvector. This distinctive feature makes systems exhibiting EPs more sensitive to external perturbations than their Hermitian counterparts, where degeneracies are nondefective diabolic points. In contrast to these widely studied cases, more complex non-Hermitian degeneracies in which the eigenvectors are only partially degenerate are poorly understood. Here, we characterize these fragmented exceptional points (FEPs) systematically from a physical perspective, and demonstrate how they can be induced into the bulk and edge spectrum of two-dimensional and three-dimensional lattice models, exemplified by non-Hermitian versions of a Lieb lattice and a higher-order topological Dirac semimetal. The design of the systems is facilitated by an efficient algebraic approach within which we provide precise conditions for FEPs that can be evaluated directly from a given model Hamiltonian. The free design of FEPs significantly opens up a new frontier for non-Hermitian physics and expands the scope for designing systems with unconventional response characteristics.
Exceptional-Point Geometry of Weak Topological Boundary States
Instituto de Estructura de la Materia (IEM-CSIC)（物质结构研究所）；Departamento de Física, Universidad Técnica Federico Santa María（圣地亚哥技术大学物理系）；Instituto de Física, Pontificia Universidad Católica de Valparaíso（天主教瓦尔帕莱索大学物理研究所）
Liouvillian Exceptional Points in Quantum Brickwork Circuits
Faculty of Mathematics and Physics, University of Ljubljana（卢布尔雅那大学数学物理学院）；Department of Physics, University of Wuppertal（伍珀塔尔大学物理系）；Dipartimento di Fisica “E.R. Caianiello”, and INFN Sezione di Napoli - Gruppo Collegato di Salerno, Università di Salerno（萨莱诺大学E.R.卡伊涅洛物理系及意大利国家核物理研究所那不勒斯分部萨莱诺协作组）
Pseudo-Hermitian Topology of Multiband Non-Hermitian Systems
Institute for Basic Science (IBS)（基础科学研究院）；Korea University of Science and Technology (UST)（韩国科学技术院）；Korea Advanced Institute of Science and Technology (KAIST)（韩国科学技术高等研究院）；Pukyong National University（釜庆国立大学）；Hanyang University（汉阳大学）
Revisiting the hierarchical construction of higher-order exceptional points
描述开放量子或波系统的非厄米哈密顿量的谱中的高阶例外点具有各种潜在的应用，特别是在光学和光子学中。然而，实验实现是出了名的困难。最近，Q. Zhong等人[Phys. Rev. Lett. 125，203602（2020）]已经引入了一种鲁棒构造，其中具有相同阶次的例外点的两个子系统的单向耦合一般导致阶次两倍的单个例外点。在这里，我们调查这一计划以不同的方式，通过利用所涉及的哈密顿量的无痕部分的幂零性。我们推广的计划，并推导出一个简单的公式的频谱响应强度的复合系统托管高阶例外点。讨论了它与子系统光谱响应强度的关系。此外，我们研究非一般扰动。最后用一个例子说明了结果。
Non-Hermitian Exceptional Topology on a Klein Bottle Photonic Circuit
KTH Royal Institute of Technology（皇家理工学院）；Stockholm University（斯德哥尔摩大学）；Rochester Institute of Technology（罗切斯特理工学院）；Huazhong University of Science and Technology（华中科技大学）
Out-of-time-ordered correlator in non-Hermitian quantum systems
研究了非厄米量子伊辛系统中的非时序关联函数（OTOC）的行为。结果表明，OTOC不仅可以诊断出Yang-Lee边奇异的基态异常点，还可以诊断出激发态的\textit{dynamical}异常点.我们发现，宇称时间对称相位下OTOC的演化可以分为两个阶段：在短时间阶段，OTOC发生周期性振荡，当参数在基态例外点附近时，这种振荡行为可以用$(0+1)$ D Yang-Lee边奇异性的标度理论和$(1+1)$ D量子伊辛模型的标度理论来描述;而在长时间阶段，OTOC受动力学异常点的控制呈指数增长。然后讨论了可能的实验实现。
Advanced Science Research Center, Japan Atomic Energy Agency（日本原子能机构先进科学研究中心）；Research Center for Nuclear Physics, The University of Osaka（大阪大学核物理研究中心）
Imaginary eigenvalues of Hermitian Hamiltonian with an inverted potential well and transition to the real spectrum at exceptional point by a non-Hermitian interaction
Amplified Memory and Finite-Time Regularity in Driven Non-Hermitian Systems
Beijing Institute of Mathematical Sciences and Applications (BIMSA)（北京数学与应用研究所）；Department of Physics, Institute for Advanced Studies in Basic Sciences (IASBS)（基础科学高等研究院物理系）；School of Quantum Physics and Matter Science, Institute for Research in Fundamental Sciences (IPM)（基本科学研究院量子物理与物质科学学院）；Max Planck Institute for the Chemical Physics of Solids（马克斯·普朗克固体化学物理研究所）
