Abstract Due to the nonunitary time evolution and possibly complex energy eigenvalues in non-Hermitian systems, it is still under debate how to properly deal with the dynamics of time-dependent non-Hermitian Hamiltonian. Recently a quantum metric framework has been proposed to study the dynamics of generated defects of a non-Hermitian system under linear quench. Here, we provide an explicit expression for the endowed Hamiltonian under quantum metric for a general two-level non-Hermitian system. Then we propose two exactly solvable models for the study of nonadiabatic dynamics of non-Hermitian systems, and analyze the defect production using the metric method. We find that, in contrast to the direct normalization method, the metric method can reproduce the symmetry of generated defects. The power-law scaling of generated defects with respect to quench time is also obtained.
Fund: Project supported by the National Key Research and Development Program of the Ministry of Science and Technology of China (Grant No. 2021YFA1200700), the National Natural Science Foundation of China (Grant Nos. 11905054 and 12275075), and the Fundamental Research Funds for the Central Universities of China.
Corresponding Authors:
Fuxiang Li
E-mail: fuxiangli@hnu.edu.cn
Cite this article:
Kangyi Hu(胡康溢), Menghua Deng(邓孟华), and Fuxiang Li(李福祥) Exactly solvable models for non-Hermitian systems under nonadiabatic quench dynamics 2025 Chin. Phys. B 34 050204
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