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Exceptional points (EPs) are degeneracies of non-Hermitian operators where, in addition to the eigenvalues, corresponding eigenmodes become degenerate. Classical and quantum photonic systems with EPs have attracted tremendous attention due…

Several works have recently addressed the emergence of exceptional points (EPs), i.e., spectral singularities of non-Hermitian Hamiltonians, in the long-wavelength dynamics of coupled magnetic systems. Here, by focusing on the driven…

Mesoscale and Nanoscale Physics · Physics 2023-01-04 Xin Li , Kuangyin Deng , Benedetta Flebus

Despite their ubiquity, a systematic classification of multifold exceptional points, $n$-fold spectral degeneracies (EP$n$s), remains a significant unsolved problem. In this article, we characterize the Abelian eigenvalue topology of…

Mesoscale and Nanoscale Physics · Physics 2025-01-30 Tsuneya Yoshida , J. Lukas K. König , Lukas Rødland , Emil J. Bergholtz , Marcus Stålhammar

In the broad context of physics ranging from classical experimental optics to quantum mechanics of unitary as well as non-unitary systems there emerge interesting phenomena related to the presence of the so called Kato's exceptional points…

Quantum Physics · Physics 2018-09-17 Miloslav Znojil

We have investigated the exceptional points (EPs) which are degeneracies of a non-Hermitian Hamiltonian, in the case that three modes are interacting with each other. Even though the parametric evolution of the modes cannot be uniquely…

Quantum Physics · Physics 2015-05-30 Jung-Wan Ryu , Soo-Young Lee , Sang Wook Kim

Non-Hermitian phenomena offer a novel approach to analyze and interpret spectra in the presence of interactions. Using the density-matrix renormalization group (DMRG), we demonstrate the existence of exceptional points for the one-particle…

Strongly Correlated Electrons · Physics 2021-02-08 Roman Rausch , Robert Peters , Tsuneya Yoshida

We develop a unified framework to classify topological defects in insulators and superconductors described by spatially modulated Bloch and Bogoliubov de Gennes Hamiltonians. We consider Hamiltonians H(k,r) that vary slowly with adiabatic…

Mesoscale and Nanoscale Physics · Physics 2011-02-28 Jeffrey C. Y. Teo , C. L. Kane

Exceptional points (EPs) in non-Hermitian photonic systems have attracted considerable research interest due to their singular eigenvalue topology and associated anomalous physical phenomena. These properties enable diverse applications…

Optics · Physics 2025-10-17 Kaiyuan Wang , Qi Jie Wang , Matthew R. Foreman , Yu Luo

Exceptional points (EPs) are peculiar band singularities and play a vital role in a rich array of unusual optical phenomena and non-Hermitian band theory. In this paper, we provide a topological classification of isolated EPs based on…

Mesoscale and Nanoscale Physics · Physics 2022-06-29 Haiping Hu , Shikang Sun , Shu Chen

Physical systems with gain and loss can be described by a non-Hermitian Hamiltonian, which is degenerated at the exceptional points (EPs). Many new and unexpected features have been explored in the non-Hermitian systems with a great deal of…

A non-Hermitian system at an exceptional point (EP), a specific critical point (CP) associated with the parity-time symmetric phase transition, exhibits a sublinear response to perturbation and promise unprecedented sensitivity beyond the…

Recent experimental efforts towards the detection of Majorana bound states have focused on creating the conditions for topological superconductivity. Here we demonstrate an alternative route, which achieves fully localised zero-energy…

Mesoscale and Nanoscale Physics · Physics 2016-03-07 Pablo San-Jose , Jorge Cayao , Elsa Prada , Ramón Aguado

Non-Hermitian degeneracies, also known as exceptional points (EPs), have been the focus of much attention due to their singular eigenvalue surface structure. Nevertheless, as pertaining to a non-Hermitian metasurface platform, the reduction…

Compared with Hermitian theory, non-Hermitian physics offers a fundamentally different mathematical framework, enabling the observation of topological phenomena that have no analogue in Hermitian systems. Among these, the exceptional point…

Quantum Physics · Physics 2025-09-24 Zhong-Sheng Chen , Wei-Xin Chen , Fan Wu , Zhong-Wei Xu , Jing Ma , Yun-Kun Jiang , Huai-Zhi Wu , Shi-Biao Zheng

Chirality is more than a geometric curiosity; it governs measurable asymmetries across nature, from enantiomer-selective drugs and left-handed fermions in particle physics to handed charge transport in Weyl semimetals. We extend this…

Quantum Physics · Physics 2025-12-23 Kyu-Won Park , KyeongRo Kim , Kabgyun Jeong

In non-Hermitian systems, the defective band degeneracies, so-called exceptional points (EPs), can form robust exceptional lines (ELs) in 3D momentum space in the absence of any symmetries. Here, we show that a natural orientation can be…

Optics · Physics 2022-12-13 Ruo-Yang Zhang , Xiaohan Cui , Wen-Jie Chen , Zhao-Qing Zhang , C. T. Chan

Exotic singular objects, known as exceptional points, are ubiquitous in non-Hermitian physics. They might be spectral singularities in energy bands that produce anomalous effects and defectiveness. The quantum entanglement of a generic…

Quantum Physics · Physics 2023-04-19 Wei-Zhu Yi , Yong-Ju Hai , Rong Xiao , Wei-Qiang Chen

We propose an analysis technique for the exceptional points (EPs) occurring in the discrete spectrum of open quantum systems (OQS), using a semi-infinite chain coupled to an endpoint impurity as a prototype. We outline our method to locate…

Quantum Physics · Physics 2012-10-16 Savannah Garmon , Ingrid Rotter , Naomichi Hatano , Dvira Segal

We identify a new kind of physically realizable exceptional point (EP) corresponding to degenerate coherent perfect absorption, in which two purely incoming solutions of the wave operator for electromagnetic or acoustic waves coalesce to a…

Optics · Physics 2019-03-12 William R. Sweeney , Chia Wei Hsu , Stefan Rotter , A. Douglas Stone

Motivated by the recent growing interest in the field of $\mathcal{P}\mathcal{T}$-symmetric Hamiltonian systems we theoretically study the emergency of singularities called Exceptional Points ($\textit{EP}$s) in the eigenspectrum of…

Quantum Physics · Physics 2023-08-15 Grigory A. Starkov , Mikhail V. Fistul , Ilya M. Eremin