Exact Solution for the Interacting Kitaev Chain at the Symmetric Point

The Kitaev chain model with a nearest neighbor interaction U is solved exactly at the symmetry point Delta = t and chemical potential mu = 0 in an open boundary condition. By applying two Jordan-Wigner transformations and a spin rotation, such a symmetric interacting model is mapped onto a noninteracting fermion model, which can be diagonalized exactly. The solutions include a topologically nontrivial phase at |U| < t and a 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.