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We investigate the robustness of Majorana edge modes under disorder andinteractions. We exploit a recently found mapping of the interacting Kitaevchain in the symmetric region ($\mu = 0$, $t = \Delta$) to free fermions.Extending the exact solution to the disordered case allows us to calculateanalytically the topological phase boundary for all interaction and disorderstrengths, which has been thought to be only accessible numerically. Wediscover a regime in which moderate disorder in the interaction matrix elementsenhances topological order well into the strongly interacting regime $U > t$.We also derive the explicit form of the many-body Majorana edge wave functionrevealing how it is dressed by many-particle fluctuations from interactions.The qualitative features of our analytical results are valid beyond thefine-tuned integrable point as expected from the robustness of topologicalorder and as corroborated here by an exact diagonalization study of smallsystems.

Robustness of Majorana edge modes and topological order -- exact results for the symmetric interacting Kitaev chain with disorder