Biorthogonal quantum criticality in non-Hermitian many-body systems

We develop the perturbation theory of the fidelity susceptibility in biorthogonal bases for arbitrary interacting non-Hermitian many-body systems with real eigenvalues.The quantum criticality in the non-Hermitian transverse field Ising chain is investigated by the second derivative of the ground-state energy and the ground-state fidelity susceptibility.We show that the system undergoes a secondorder phase transition with the Ising universal class by numerically computing the critical points and the critical exponents from the finite-size scaling theory.Interestingly,our results indicate that the biorthogonal quantum phase transitions are described by the biorthogonal fidelity susceptibility instead of the conventional fidelity susceptibility.