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    Survival of Hermitian criticality in the non-Hermitian framework

    Fei Wang1, Guoying Liang1, Zecheng Zhao1, Lin-Yue Luo2,3, Da-Jian Zhang4,*, and Bao-Ming Xu1,†

    • 1Institute of Biophysics, Dezhou University, Dezhou 253023, China
    • 2Key Laboratory of Atomic and Subatomic Structure and Quantum Control (Ministry of Education), Guangdong Basic Research Center of Excellence for Structure and Fundamental Interactions of Matter, School of Physics, South China Normal University, Guangzhou 510006, China
    • 3Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Frontier Research Institute for Physics, South China Normal University, Guangzhou 510006, China
    • 4Department of Physics, Shandong University, Jinan 250100, China

    • *Contact author: zdj@sdu.edu.cn
    • †Contact author: xubm2018@163.com

    Phys. Rev. B 113, 165149 – Published 27 April, 2026

    DOI: https://doi.org/10.1103/y34y-32dt

    Abstract

    In this work, we investigate many-body phase transitions in a one-dimensional anisotropic XY model subject to a complex-valued transverse field. Within the biorthogonal framework, we calculate the ground-state correlation functions and entanglement entropy, confirming that their scaling behavior remains identical to that in the Hermitian XY model. The preservation of Hermitian phase transition features in the non-Hermitian setting is rooted in the persistence and emergence of symmetries and their breaking. Specifically, the ferromagnetic (FM) phase arises from the breaking of a Z2 symmetry, while the Luttinger liquid (LL) phase is enabled by the emergence of a U(1) symmetry together with the degeneracy of the real part of the energy spectrum. The nontrivial topology of the LL phase is characterized by the winding number around the exceptional point (EP). Given that non-Hermitian systems are inherently open, our findings suggest a new avenue for exploring universal critical phenomena associated with conventional quantum phase transitions, which are typically vulnerable to decoherence and environmental disruption in conventional open quantum systems.

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