Parent Hamiltonian and intrinsic phase transition in non-Hermitian photonic systems

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 (AKLT) 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 work 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.

9 pages, 5 figures. Accepted for publication in Physical Review Letters

Quantum Physics (quant-ph); Mesoscale and Nanoscale Physics (cond-mat.mes-hall)

arXiv:2607.28964 [quant-ph]

(or arXiv:2607.28964v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2607.28964 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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