Exact Solution to Interacting Kitaev Chain at Symmetric Point

TL;DR

This paper presents an exact solution for an interacting Kitaev chain at a symmetric point, revealing topological phases and quantum phase transitions through a novel mapping to a non-interacting fermion model.

Contribution

It introduces an exact analytical solution for the interacting Kitaev chain at a specific symmetric point, enabling detailed analysis of topological phases and phase transitions.

Findings

Identification of topologically non-trivial phase for |U|<t

Identification of topologically trivial phase for |U|>t

Exact diagonalization of the model at the 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.