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Recently, the two-site Kitaev model hosting Majorana edge states wasexperimentally realized based on double quantum dots. In this context, weconstruct two-band effective models describing Majorana edge states of afinite-length Kitaev chain by using the isospectral matrix reduction method. Weanalytically estimate the robustness of Majorana edge states as a function ofmodel parameters. We also study effects of coupling to an environment based onnon-Hermitian Hamiltonians derived from the Lindblad equation. We study threetypes of dissipation, a local one, an adjacent one and a global one. It isfound that the Majorana zero-energy edge states acquire nonzero energy such as$E\propto \pm \left( i\gamma \right) ^{L}$ for the local dissipation, where$\gamma $ is the magnitude of the dissipation and $L$ is the length of thechain. On the other hand, the Majorana zero-energy edge states acquire nonzeroenergy such as $E\propto \pm i\gamma $ irrespective of the length $L$ for theglobal dissipation. Hence, the Majorana edge states are robust against thelocal dissipation but not against the global one. Our results will be usefulfor future studies on Majorana edge states based on quantum dots.

Robustness of Majorana edge states of short-length Kitaev chains coupled with environment