In this work, we study the adiabatic phases and shortcut for a pseudo-Hermitian interacting spin-1/2 composite system in which one system is driven by a non-Hermitian magnetic field. The biorthonormal eigenbasis and the condition for real eigenvalues have been derived and discussed. By studying the Berry phases and the transitionless quantum driving (TQD) Hamiltonian, the roles of correlation between the subsystems and the non-Hermicity are discussed. The non-Hermitian dynamics and the Berry phases of the subsystem, as well as their influences on the TQD Hamiltonian are studied in both no correlation and large correlation cases. These results mean that we can modify the correlation between the subsystems to control the adiabatic shortcuts of the subsystems. These schemes can provide a feasible way for studying the adiabatic shortcuts of the composite system and the non-Hermitian system.

中文翻译：

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伪-厄米复合系统的绝热演化和捷径

在这项工作中，我们研究了伪厄米相互作用自旋 1/2 复合系统的绝热相和捷径，其中一个系统由非厄米磁场驱动。已经推导出并讨论了双正交特征基础和实特征值的条件。通过研究 Berry 相和无跃迁量子驱动 (TQD) 哈密顿量，讨论了子系统和非 Hermicity 之间相关性的作用。在无相关和大相关情况下研究了子系统的非厄米动力学和 Berry 相，以及它们对 TQD 哈密顿量的影响。这些结果意味着我们可以修改子系统之间的相关性来控制子系统的绝热捷径。