Probing topological phase transition with non-Hermitian perturbations

We demonstrate that non-Hermitian perturbations can probe topological phase transitions and unambiguously detect non-Abelian zero modes. We show that under carefully designed non-Hermitian perturbations, the Loschmidt echo(LE) decays into 1/N where N is the ground state degeneracy in the topological non-trivial phase, while it approaches 1 in the trivial phase. This distinction is robust against small parameter deviations in the non-Hermitian perturbations. We further study four well-known models that support Majorana or parafermionic zero modes. By calculating their dynamical responses to specific non-Hermitian perturbations, we prove that the steady-state LE can indeed differentiate between different phases. This method avoids the ambiguity introduced by trivial zero-energy states and thus provides an alternative and promising way to demonstrate the emergence of topologically non-trivial phases. The experimental realizations of non-Hermitian perturbations are discussed.