Exact zero modes in twisted Kitaev chains

@article{Kawabata2017ExactZM,
  title={Exact zero modes in twisted Kitaev chains},
  author={Kohei Kawabata and Ryohei Kobayashi and Ning Wu and Hosho Katsura},
  journal={Physical Review B},
  year={2017},
  volume={95},
  pages={195140}
}
We study the Kitaev chain under generalized twisted boundary conditions, for which both the amplitudes and the phases of the boundary couplings can be tuned at will. We explicitly show the presence of exact zero modes for large chains belonging to the topological phase in the most general case, in spite of the absence of ``edges'' in the system. For specific values of the phase parameters, we rigorously obtain the condition for the presence of the exact zero modes in finite chains, and show… 

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