The spectral, dynamical and topological properties of physical systems described by non-Hermitian (including $\mathcal{PT}$-symmetric) Hamiltonians are deeply modified by the appearance of exceptional points and spectral singularities. Here we show that exceptional points in the continuum can arise in non-Hermitian (yet admitting and entirely real-valued energy spectrum) optical lattices with engineered defects. At an exceptional point, the lattice sustains a bound state with an energy embedded in the spectrum of scattered states, similar to the von-Neumann Wigner bound states in the continuum of Hermitian lattices. However, the dynamical and scattering properties of the bound state at an exceptional point are deeply different from those of ordinary von-Neumann Wigner bound states in an Hermitian system. In particular, the bound state in the continuum at an exceptional point is an unstable state that can secularly grow by an infinitesimal perturbation. Such properties are discussed in details for transport of discretized light in a $\mathcal{PT}$-symmetric array of coupled optical waveguides, which could provide an experimentally accessible system to observe exceptional points in the continuum.
Exceptional-point-constrained locking of boundary-sensitive topological transitions in chiral non-Hermitian SSH-type lattices
Institute of Theoretical Physics and State Key Laboratory of Quantum Optics Technologies and Devices, Shanxi University（山西大学理论物理研究所与量子光学技术与器件国家重点实验室）；Department of Physics, Fudan University（复旦大学物理系）
PT-symmetry breaking with divergent potentials: lattice and continuum cases
研究了在连续极限下，长程、非厄米、$\mathcal{PT}$对称势保持有限或发散时，格点模型中的宇称和时间反演（$\mathcal{PT}$）对称性破缺.通过对开放有限格点的脆弱$\mathcal{PT}$阈值的标度分析，我们证明了连续损失-增益势$V_α(x)\propto i |x|^α\mathrm{sign}(x)$对$α>-2$有正的$\mathcal{PT}$ -破缺阈值，对$α\leq -2$有零阈值.当$α<0$局域态具有复杂的（共轭）能量的连续带中出现在较高的损失增益强度。我们研究了耦合波导中$\mathcal{PT}$对称性破缺的特征，发现局域态的出现大大缩短了$\mathcal{PT}$对称性破缺区域的时间尺度.
Continuum limit of lattice quasielectron wavefunctions
描述劳克林态中任意准空穴的试验态很早就被发现了，因此很自然地期望人们也应该能够创造任意准电子。然而，现有的准电子的试探波函数显示出与预期的拓扑性质不兼容的行为，或者它们的构造涉及特设元素。然而，研究表明，对于晶格分数量子霍尔系统，有可能找到一个相对简单的准电子波函数，它具有所有预期的性质[New J. Phys. 20，033029（2018）]。这自然提出了一个问题：这个波函数在连续极限中会发生什么？在这里，我们证明，虽然一个有限的连续波函数时，准电子是在顶部的晶格网站，这样的限制晶格准电子一般不存在。特别是，如果准电子被放置在晶格位置以外的任何地方，当接近连续极限时，晶格波函数发散。发散可以通过将状态投影到最低的朗道能级上来消除，但是我们发现投影的状态也不具有任何准电子所期望的性质。因此，我们的结论是，晶格准电子波函数并没有解决困难的任何准电子在连续找到试验状态。
Anomalous transport in quasiperiodic lattices: emergent exceptional points at band edges and log-periodic oscillations
Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所凝聚态物理国家实验室）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）
