Probing topological phase transition with non-Hermitian perturbations

We demonstrate that non-Hermitian perturbation can probe topological phase transitions and unambiguously detect non-Abelian zero modes. We show that under the non-Hermitian fermionic parity changing perturbations, the Loschmidt echo(LE) decays into the inverse of the ground state degeneracy in the topological non-trivial phase, while it is close to one in the trivial phase. This distinction is robust against small deviations in the non-Hermitian fermionic parity changing perturbations. We further study three well-known models with such specific non-Hermitian perturbations. By calculating their dynamical responses, we prove that the steady-state LE can indeed be used to differentiate different phases. This method avoids the ambiguity brought by the trivial zero energy states and thus can demonstrate the emergence of topological non-trivial phases. The experimental realizations of non-Hermitian perturbations are discussed.