Effective non Hermitian physics for degenerate ground states of a non Hermitian Ising model with \mathcal{RT} symmetry
In this paper, based on a one dimensional non Hermitian spin model with \mathcal{RT} invariant term, we study the non Hermitian physics for the two (nearly) degenerate ground states. By using the high order perturbation method, an effective pseudo spin model is obtained to describe non Hermitian physics for the two (nearly) degenerate ground states, which are precisely consistent with the numerical calculations. We found that there may exist effective (anti) \mathcal{PT} symmetry for the effective pseudo spin model of the two (nearly) degenerate ground states. In particular, there exists spontaneous (anti) \mathcal{PT} symmetry breaking for the topological degenerate ground states with tunable parameters in external fields. We also found that even a very tiny imaginary external field applied will drive \mathcal{PT} phase transition.