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A moir\'{e} pattern occurs when two periodic structures in a system have aslight mismatch period, resulting the coexistence of distinct phases indifferent large-scale spacial regions of the same system. Two periodicstructures can arise from periodic electric and magnetic fields, respectively.We investigated the moir\'{e} pattern via a dimerized Kitaev spin chain with aperiodic transverse field, which can be mapped onto the system of dimerizedspinless fermions with p-wave superconductivity. The exact solution forstaggered field demonstrated that the ground state has two distinct phases: (i)Neel magnetic phase for nonzero field, (ii) Spin liquid phase due to theemergence of isolated flat Bogoliubov--de Gennes band for vanishing field. Wecomputed the staggered magnetization and local density of states(\textrm{LDOS}) for the field with a slight difference period to the chainlattice. Numerical simulation demonstrated that such two phases appearalternatively along the chain with a long beat period. Additionally, weproposed a dynamic scheme to detect the Moir\'{e} fringes based on themeasurement of Loschmidt echo (\textrm{LE}) in the presence of localperturbation.

Moir\'{e} pattern of spin liquid and Neel magnet in a Kitaev chain