Non-Hermitian avalanche effect: Non-perturbative effect induced by local non-Hermitian perturbation on a Z2topological order

In this paper, based on a non-Hermitian toric-code model we found the fragileness of intrinsic topological orders under non-Hermitian perturbations. The effect of non-Hermitian avalanche for a designed toric-code model is uncovered: for the designed toric-code model with special external fields, a tiny non-Hermitian perturbation (local imaginary state-selective dissipation) leads to anomalous topological degeneracy and breaks down the bulk-degeneracy correspondence (a correspondence between bulk quasi-particles and topologically protected degenerate ground states). To support our theoretical predictions, we calculated the ground-state degeneracy and fidelity susceptibility of the ground states based on the non-Hermitian toric-code model on $2*2*2$ lattice and that on $2*3*3$ lattice. The numerical results are consistent with theoretical prediction.