Exact Solution to Interacting Kitaev Chain at Symmetric Point

Abstract

Kitaev chain model with nearest neighbor interaction U is solved exactly at the symmetry point $\Delta =t$ and chemical potential $\mu =0$ in open boundary condition. By applying two Jordan-Wigner transformations and a spin-rotation, such a symmetric interacting model is mapped to a non-interacting fermion model, which can be diagonalized exactly. The solutions include topologically non-trivial phase at $|U|<t$ and topologically trivial phase at $|U|>t$. The two phases are related by dualities. Quantum phase transitions in the model are studied with the help of the exact solution.

10 pages, 1 figure

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