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

Abstract

By using the variational matrix product state method, we numerically study the interacting Kitaev chain with spatially varying periodic and quasiperiodic potentials, and the latter follows the Fibonacci sequence. The edge correlation functions of Majorana fermions and low-lying ground states are computed to explore the robustness of topological superconducting phase. It is found that the original topologically nontrivial phase is separated into two branches by an emergent topologically trivial phase, as a result of the competition among spatially varying potential, electronic, Coulomb interaction, and chemical potential. The analysis of energy gap, occupation number, and intertwined string order parameters together suggests that the lift of degeneracy in the topologically trivial phase is enabled by a potential-induced fracton mechanism, namely, the pairing of four Majorana fermions. The evolution from the emergent fractal structure of population to the original structure of charge density wave is investigated as well.