A topologically equivalent tight binding model is proposed to study the quantum phase transitions of dimer chain driven by an imaginary alternating field. I demonstrate how the partner Hamiltonian is constructed by a similarity transformation to fulfil the $\mathcal{PT}$ symmetry. The $\mathcal{PT}$ symmetry of the partner model allows us to study the topological properties of the original non-Hermitian model as the Bloch bands of the Hermitian system. The quantum phase transitions are discussed in different frequency regime. The approach has the potential applications to investigate the topological states of matter driven by the complex external parameters.

中文翻译：

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由虚交变场驱动的二聚体链的量子相变

提出了拓扑等效紧束缚模型来研究由假想交变场驱动的二聚体链的量子相变。我演示了如何通过相似变换构造伙伴哈密顿量来满足$\mathcal{PT}$对称。这$\mathcal{PT}$伙伴模型的对称性使我们能够将原始非厄米模型的拓扑性质研究为厄米系统的布洛赫带。在不同的频率范围内讨论了量子相变。该方法具有研究由复杂外部参数驱动的物质拓扑状态的潜在应用。