There are various research strategies used for non-Hermitian systems, which typically involve introducing non-Hermitian terms to preexisting Hermitian Hamiltonians. It can be challenging to directly design non-Hermitian many-body models that exhibit unique features not found in Hermitian systems. In this Letter, we propose a new method for constructing non-Hermitian many-body systems by generalizing the parent Hamiltonian method into non-Hermitian regimes. This allows us to build a local Hamiltonian using given matrix product states as its left and right ground states. We demonstrate this method by constructing a non-Hermitian spin-1 model from the asymmetric Affleck-Kennedy-Lieb-Tasaki state, which preserves both chiral order and symmetry-protected topological order. Our approach opens up a new paradigm for systematically constructing and studying non-Hermitian many-body systems, providing guiding principles for exploring new properties and phenomena in non-Hermitian physics.

中文翻译：

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从矩阵积态构造非厄米特父哈密顿量

用于非厄米系统的研究策略有多种，通常涉及向预先存在的厄米哈密顿量引入非厄米项。直接设计具有厄米系统中未发现的独特特征的非厄米多体模型可能具有挑战性。在这封信中，我们提出了一种通过将父哈密顿方法推广到非厄米体系中来构造非厄米多体系统的新方法。这允许我们使用给定的矩阵乘积状态作为其左右基态来构建局部哈密顿量。我们通过从不对称的 Affleck-Kennedy-Lieb-Tasaki 态构建非厄米自旋 1 模型来演示该方法，该模型保留了手性顺序和对称保护的拓扑顺序。