Intertwined string orders of topologically trivial and nontrivial phases in an interacting Kitaev chain with spatially varying potentials

By using the variational matrix product state method, we numerically study\nthe interacting Kitaev chain with spatially varying periodic and quasi-periodic\npotentials and the latter follows the Fibonacci sequence. The edge correlation\nfunctions of Majorana fermions and low-lying ground states are computed to\nexplore the robustness of topological superconducting phase. It is found that\nthe original topological nontrivial phase is separated into to two branches by\nan emergent topological trivial phase, as a result of the competition among\nspatially varying potential, electronic Coulomb interaction and chemical\npotential. The analysis of energy gap and occupation number together suggests\nthat the spontaneous symmetry breaking and the lift of degeneracy in the\ntopological trivial phase are enabled by a potential-induced Fracton mechanism,\nnamely the pairing of four Majorana fermions. It can be broken by further\nenhancing the interaction, and then the nontrivial phase reemerges. The\nevolution from the emergent fractal structure of population outside the\ncritical region to the original structure of charge density wave is\ninvestigated as well.\n