The dynamics described by the non-Hermitian Hamiltonian typically capture the short-term behavior of open quantum systems before quantum jumps occur. In contrast, the long-term dynamics, characterized by the Lindblad master equation (LME), drive the system towards a non-equilibrium steady state (NESS), which is an eigenstate with zero energy of the Liouvillian superoperator, denoted as L. Conventionally, these two types of evolutions exhibit distinct dynamical behaviors. However, in this study, we challenge this common belief and demonstrate that the effective non-Hermitian Hamiltonian can accurately represent the long-term dynamics of a critical two-level open quantum system. The criticality of the system arises from the exceptional point (EP) of the effective non-Hermitian Hamiltonian. Additionally, the NESS is identical to the coalescent state of the effective non-Hermitian Hamiltonian. We apply this finding to a series of critical open quantum systems and show that a local dissipation channel can induce collective alignment of all spins in the same direction. This direction can be well controlled by modulating the quantum jump operator. The corresponding NESS is a product state and maintains long-time coherence, facilitating quantum control in open many-body systems. This discovery paves the way for a better understanding of the long-term dynamics of critical open quantum systems.

张禧征，天津师范大学物理与材料科学学院教授，博士生导师。2014年博士毕业于南开大学，随后在北京计算科学研究中心、新加坡国立大学物理系从事博士后研究工作，2015年、2018年分别赴南开大学陈省身数学研究所、美国罗彻斯特大学交流访问。主要从事量子物理与凝聚态理论的研究，在Physical Review系列等杂志上发表论文50余篇,引用1000余次。担任Physical Review A\B Letter的评审人。主持国家自然科学基金面上项目2项，主持完成国家自然科学基金青年基金项目1项，国际合作交流项目1项，理论物理专项1项。获批天津市中青年骨干创新人才计划，131人才二层次。