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Next-nearest-neighbor Heisenberg chain plays important roles in solid statephysics, such as predicting exotic electric properties of two-dimensionalmaterials or magnetic properties of organic compounds. Direct experimentalstudies of the many-body electron systems or spin systems associating to thesematerials are challenging tasks, while optical simulation provides an effectiveand economical way for immediate observation. Comparing with bulk optics,integrated optics are more of fascinating for steady, large scale and long-timeevolution simulations. Photonic crystal is an artificial microstructurematerial with multiple methods to tune the propagation properties, which areessential for various simulation tasks. Here we report for the first time anexperimental simulation of next-nearest-neighbor Heisenberg chain with anintegrated optical chip of photonic crystal waveguide array. The use ofphotonic crystal enhances evanescent field thus allows coupling betweennext-nearest-neighbor waveguides in such a planar waveguide array, withoutbreaking the weak coupling condition of the coupled mode equation.Particularly, similarities between the model and coherent light propagationcould reach 0.99 in numerical simulations and 0.89 in experiment. Localizationeffect induced by second-order coupling and coupling strengthening withincreasing wavelengths were also revealed in both numerical simulations andexperiments. The platform proposed here is compatible with mature complementarymetal oxide semiconductor technology thus possesses the potential forlarger-scale problems and photonic crystals further allows simulations ofspecific target Hamiltonians.

Experimental simulation of next-nearest-neighbor Heisenberg chain with photonic crystal waveguide array