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By using the variational matrix product state method, we numerically studythe interacting Kitaev chain with spatially varying periodic and quasi-periodicpotentials and the latter follows the Fibonacci sequence. The edge correlationfunctions of Majorana fermions and low-lying ground states are computed toexplore the robustness of topological superconducting phase. It is found thatthe original topological nontrivial phase is separated into to two branches byan emergent topological trivial phase, as a result of the competition amongspatially varying potential, electronic Coulomb interaction and chemicalpotential. The analysis of energy gap and occupation number together suggeststhat the spontaneous symmetry breaking and the lift of degeneracy in thetopological trivial phase are enabled by a potential-induced Fracton mechanism,namely the pairing of four Majorana fermions. It can be broken by furtherenhancing the interaction, and then the nontrivial phase reemerges. Theevolution from the emergent fractal structure of population outside thecritical region to the original structure of charge density wave isinvestigated as well.

Critical region of topological trivial and nontrivial phases in interacting Kitaev chain with spatially varying potentials