Abstract
We study the extended Kitaev chain with both nearest-neighbor and next-nearest-neighbor hopping terms and find the model system exhibiting nontrivial phases, which can be characterized by a nonzero Berry phase and winding number when the system is in a pure state. While in a mixed state, we investigate the robustness of the topological Uhlmann phases and show how it responses to the presence of next-nearest-neighbor hopping terms. Furthermore, we analyse the complicated behavior of the Uhlmann phase of the extended Kitaev chain at finite temperature as k moves along the Brillouin zone, and we think this may serve as a topological indicator for mixed states in condensed matter systems.
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