General properties of fidelity susceptibility in non-Hermitian systems with PT-symmetry

We systematically derive the general properties of the fidelity susceptibility defined by the left and right many-body eigenstates of non-Hermitian Hamiltonian with the combination of parity and time-reversal symmetries (PT-symmetry). In the spontaneous PT-symmetry broken phase, we prove the fidelity susceptibility is real and diverges to negative infinity as the parameter approaches the exceptional points (EPs). This divergence leads to a significant enhancement of the fidelity susceptibility near the phase transition point in a Hermitian system with small non-Hermitian perturbations, where the phase transition point splits into a pair of EPs. We demonstrate these behaviors by the two-legged Su-Schrieffer-Heeger model with PT non-Hermitian perturbations. In addition, we find there is an emergent PT-symmetric region from the PT broken phase due to the finite size effect.