Quantum phase transitions also occur in non-Hermitian systems. In this work we show that density functional theory, for the first time, uncovers universal behaviors for phase transitions in non-Hermitian many-body systems. To be specific, we first prove that the non-degenerate steady state of a non-Hermitian quantum many-body system is a universal function of the first derivative of the steady state energy with respect to the control parameter. This finding has far-reaching consequences for non-Hermitian systems: (i) It bridges the nonanalytic behavior in physical observable and nonanalytic behavior of steady state energy, which explains why the quantum phase transitions in non-Hermitian systems occur for finite systems. (ii) It predicts universal scaling behaviors of any physical observable at non-Hermitian phase transition point with scaling exponent being $(1-1/p),2(1-1/p),\cdots,n(1-1/p),\cdots$ with $p$ being the number of coalesced states at the exceptional point and $n$ being a positive integer. (iii). It reveals that quantum entanglement in non-Hermitian phase transition point presents universal scaling behaviors with critical exponents being $(1-1/p),2(1-1/p),\cdots,n(1-1/p),\cdots$. These results uncover universal critical behaviors in non-Hermitian phase transitions and provide profound connections between entanglement and phase transition in non-Hermitian quantum many-body physics and establish foundations for quantum metrology in non-Hermitian systems.
Survival of Hermitian Criticality in the Non-Hermitian Framework
Institute of Biophysics, Dezhou University（德州大学生物物理研究所）；Key Laboratory of Atomic and Subatomic Structure and Quantum Control (Ministry of Education), Guangdong Basic Research Center of Excellence for Structure and Fundamental Interactions of Matter, School of Physics, South China Normal University（华南师范大学物理学院原子与亚原子结构及量子控制教育部重点实验室、广东省基础与应用基础研究基金委物质结构与基本相互作用卓越研究中心）；Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Frontier Research Institute for Physics, South China Normal University（华南师范大学前沿物理研究院广东省量子工程与量子材料重点实验室、广东省量子物质粤港联合实验室）；Department of Physics, Shandong University（山东大学物理学院）
Universal quantum Fisher information and simultaneous occurrence of Landau-class and topological-class transitions in non-Hermitian Jaynes-Cummings models
Singapore University of Technology and Design（新加坡科技设计大学）；National University of Singapore（新加坡国立大学）；Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area (Guangdong)（粤港澳大湾区量子科学中心（广东））
Topology and edge modes surviving criticality in non-Hermitian Floquet systems
College of Physics and Optoelectronic Engineering, Ocean University of China（中国海洋大学物理与光电工程学院）；Qingdao Key Laboratory of Advanced Optoelectronics（青岛先进光学重点实验室）；Engineering Research Center of Advanced Marine Physical Instruments and Equipment of MOE（教育部海洋高端装备工程研究中心）
Anyon-Induced Criticality and Dynamical Stability in Non-Hermitian Many-Body Systems
Singapore University of Technology and Design（新加坡科技设计大学）；Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area (Guangdong)（粤港澳大湾区量子科学中心（广东））；National University of Singapore（新加坡国立大学）
Topological characterization of phase transitions and critical edge states in one-dimensional non-Hermitian systems with sublattice symmetry
Ocean University of China（中国海洋大学）；Key Laboratory of Optics and Optoelectronics（光学与光电子学重点实验室）；Engineering Research Center of Advanced Marine Physical Instruments and Equipment of MOE（教育部先进海洋物理仪器和设备工程研究中心）
Real critical exponents from the $\varepsilon$-expansion in an interacting $U(1)$ model with non-Hermitian $Z_4$ anisotropy
Institute for Theoretical Solid State Physics, IFW Dresden（德累斯顿亥姆霍兹中心IFW固体物理研究所）；Bogolyubov Institute for Theoretical Physics（博戈留博夫理论物理研究所）；Institute for Theoretical Physics and Würzburg-Dresden Cluster of Excellence ct.qmat, TU Dresden（德累斯顿工业大学理论物理研究所与维尔茨堡-德累斯顿卓越集群ct.qmat）
