Non-Hermitian systems exhibit many unique properties, particularly the phenomena near exceptional points, which have garnered significant attention. In this work, we obtain an exact solution for a one-dimensional non-Hermitian XY model with Dzyaloshinsky-Moriya (DM) interaction, focusing on its quantum entanglement and chiral critical phenomena. Our results reveal that the DM interaction breaks the system's rotation-time-reversal symmetry and quasi-long-range order, leading to the emergence of two distinct chiral phases and a quantum critical point (QCP). The DM interaction is found to enhance the entanglement entropy in chiral phases I and II, whereas it leaves the entropy unchanged in the paramagnetic phase. Notably, the entanglement entropy exhibits a crossover behavior in the vicinity of the QCP. Furthermore, we investigate the critical behavior of the chiral order parameter near the QCP, establishing a relation between the chiral critical exponent $\theta$ and the magnetization exponent $\beta$ as $\theta =2\beta$. A key finding is that while entanglement entropy solely characterizes the transition at the QCP, the chiral order parameter serves as a more universal probe, identifying transitions at both the exceptional point and the QCP.

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• Critical phenomena
• Order parameters
• Phase diagrams
• Quantum information theory
• Quantum phase transitions
• 1-dimensional spin chains
• Exact solutions for many-body systems