Raw data for “Parent Hamiltonian and intrinsic phase transition in non-Hermitian photonic systems”

Non-Hermitian systems host phenomena absent in Hermitian physics, but realizing Hamiltonians with intrinsic non-Hermitian properties remains challenging. Here, we report the experimental generation of non-Hermitian parent Hamiltonians (NH-PHs) with tailored properties. Specifically, we use matrix product states (MPSs) to represent asymmetric Affleck-Kennedy-Lieb-Tasaki (AKLT) states that define an NH-PH. This construction is validated with single photons via two approaches: (i) imaginary-time evolution governed by the generated NH-PH to obtain its left and right ground states, and (ii) direct preparation of AKLT states by mapping the MPSs onto quantum circuits. We further characterize the properties of the system by measuring four different order parameters, where results from two methods show excellent agreement, confirming the validity of our approach. Extending the framework to larger systems, we observe a phase transition intrinsic in non-Hermitian systems where the biorthogonal zero-energy modes are no longer the global ground states. Our work provides the first experimental realization and characterization of non-Hermitian systems with controllable and customizable properties, opening new avenues for exploring novel properties and phenomena in non-Hermitian physics.