Fate of Majorana zero modes in a one-dimensional superconductor with fixed charge

While the properties of Majorana zero modes are well understood within BCS mean-field theory, it remains an ongoing challenge to demonstrate these excitations in a real condensed-matter setting. Since such systems have a fixed number of particles, it is a closely-related theoretical question whether the exponential localization and non-Abelian statistics of Majorana particles survive in a manifestly particle number conserving regime. Utilizing combinatorial arguments, we analytically study an interacting, number-conserving model on a single wire that shows signatures of topological edge excitations in edge-to-bulk correlation functions and its entanglement spectrum. With exact diagonalization and DMRG, we numerically explore an exchange and braiding protocol to verify whether the number-conserving quasiparticles show non-trivial statistics.