Critical phase transitions contain a variety of deep and universal physics, and are intimately tied to thermodynamic quantities through scaling relations. Yet, these notions are challenged in the context of non-Hermiticity, where spatial or temporal divergences render the thermodynamic limit ill-defined. In this work, we show that a thermodynamic grand potential can still be defined in pseudo-Hermitian Hamiltonians, and can be used to characterize aspects of criticality unique to non-Hermitian systems. Using the non-Hermitian Su-Schrieffer-Heeger (SSH) model as a paradigmatic example, we demonstrate the fractional order of topological phase transitions in the complex energy plane. These fractional orders add up to the integer order expected of a Hermitian phase transition when the model is doubled and Hermitianized. More spectacularly, gap preserving highly degenerate critical points known as non-Bloch band collapses possess fractional order that are not constrained by conventional scaling relations, testimony to the emergent extra length scale from the skin mode accumulation. Our work showcases that a thermodynamic approach can prove fruitful in revealing unconventional properties of non-Hermitian critical points.
Scaling of Quantum Geometry Near the Non-Hermitian Topological Phase Transitions
Institute of Atomic and Molecular Sciences, Academia Sinica（中央研究院原子与分子科学研究所）；Department of Physics, National Taiwan Normal University（台湾师范大学物理系）；Physics Division, National Center for Theoretical Sciences（国家理论科学中心物理组）
Dissipation-Induced Deviations from Kibble-Zurek Scaling in Non-Hermitian Quantum Annealing
Sharif University of Technology（谢里夫理工大学）；Institute for Advanced Studies in Basic Sciences (IASBS)（基础科学高等研究所）；Institute for Research in Fundamental Sciences (IPM)（基本科学研究院）
Equilibrium and nonequlibrium scaling behaviors of localization transition in a non-Hermitian Aubry-André model with onsite gain and loss
The School of Mathematics and Physics, Jiangsu University of Technology（江苏理工学院数学与物理学院）；The Jiangsu Key Laboratory of Clean Energy Storage and Conversion, Jiangsu University of Technology（江苏理工学院清洁能源存储与转化江苏省重点实验室）；Jiangsu Physical Science Research Center（江苏物理科学研究中心）
Equilibrium Thermodynamics of Non-Hermitian Dirac Fermions: Caloric and Magnetic Responses
Facultad de Ingeniería, Universidad San Sebastián（圣塞巴斯蒂安大学工程学院）；Departamento de Física, Universidad Técnica Federico Santa María（智利联邦理工大学物理系）；Instituto de Física, Pontificia Universidad Católica de Valparaíso（天主教瓦尔帕莱索大学物理研究所）
Effective Hamiltonian description on monitored Majorana chains: correlated power-law hoppings and unconventional entanglement scaling
University of Tokyo（东京大学）；RIKEN Pioneering Research Institute (PRI)（理化学研究所先锋研究本部）；University of Warwick（华威大学）；RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS)（理化学研究所交叉理论与数学科学中心）；RIKEN（理化学研究所）；Ritsumeikan University（立命馆大学）
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。
Measurement-induced dark state phase transitions in long-ranged fermion systems
我们确定了一个非常规的代数标度阶段的量子动力学的自由费米子与长程跳跃，这是暴露于连续的局部密度测量。非常规阶段的特征在于代数纠缠熵增长，并通过缓慢的代数衰减的密度-密度关联函数，都与分数指数。它发生在跳变衰减指数$1< p \lesssim 3/2$上，与测量速率无关。代数相产生两条临界线，将其与小的对数纠缠增长的临界相和大的监测速率下的恒定纠缠熵的面积律相分开。微扰的重整化群分析表明，过渡到长程相位也是非常规的，对应于修改后的正弦戈登理论。将监测到的波函数的精确数值模拟与副本场论方法的分析预测进行比较，得到了极好的定量一致性。这证实了测量引起的相变作为量子相变在一个有效的，非厄米哈密顿暗态的观点。
