Local symmetry enhanced Majorana zero modes in one-dimensional fermionic systems with particle-number preserving interactions

The realization and manipulation of topological Majorana zero modes (MZMs) have been pivotal in both theoretical and experimental research. In this paper, we present a symmetry enhanced topological model that supports stable, localized MZMs in a one-dimensional interacting fermionic system. The MZMs in our model, induced by particle-number conserving interactions, are fully decoupled from the chain's interior and remain degenerate regardless of chain length, allowing for simulations in extremely short fermionic chains. The topological phase transition is driven by changes in coupling parameters, transitioning to a trivial phase without affecting the MZMs' independence or degeneracy, only their topological protection. Additionally, local symmetries in the model enhance MZMs' stability and reveal unique odd-even effects across different chain lengths.