Entanglement, non-Hermiticity and duality

A rigorous duality is established to diagnose entanglement structure of non-Hermitian systems. During the duality process, entanglement spectrum and entanglement entropy keep invariant but Hermiticity may be substantially altered. We classify non-Hermitian models into two types. In type-I exemplified by the "non-reciprocal lattice model", there exists at least one duality map that sends the original non-Hermitian model to a Hermitian model. In other words, entanglement structure of type-I non-Hermitian models is entirely controlled by Hermitian models. Therefore, known results of entanglement of Hermitian systems can be efficiently applied to type-I non-Hermitian systems. On the other hand, dual systems of type-II, exemplified by "non-Hermitian Su-Schrieffer-Heeger model", are always non-Hermitian. We further notice that non-Hermitian systems with complex entanglement spectrum is of type-II but the inverse is not true. In summary, the entanglement diagnosis proposed in this Letter bridges non-Hermitian and Hermitian systems, shedding light on classification and characterization of generic non-Hermitian systems via entanglement. Several promising directions of future work are proposed.