  We study the effects of disorder on a Kitaev chain with longer-range hopping
and pairing terms which is capable of forming local zero energy excitations
and, hence, serves as a minimal model for localization-protected edge qubits.
The clean phase diagram hosts regions with 0, 1, and 2 Majorana zero-modes
(MZMs) per edge. Using a semi-analytic approach corroborated by numerical
calculations of the entanglement degeneracy, we show how phase boundaries
evolve under the influence of disorder. While in general the 2 MZM region is
stable with respect to moderate disorder, stronger values drive transition
towards the topologically trivial phase. We uncover regions where the addition
of disorder induces local zero-modes absent for the corresponding clean system.
Interestingly, we discover that disorder destroys any direct transition between
phases with zero and two MZMs by creating a tricritical point at the 2-0 MZM
boundary of the clean system. Finally, motivated by recent experiments, we
calculate the characteristic signatures of the disorder phase diagram as
measured in dynamical local and non-local qubit correlation functions. Our work
provides a minimal starting point to investigate the coherence properties of
local qubits in the presence of disorder.
