Quantum Criticality of a Periodically Driven Non-Hermitian Su–Schrieffer–Heeger System

Quantum fidelity can serve as an effective diagnostic tool for detecting topological phase transitions. We investigate quantum critical behavior and topological phase transitions in a one-dimensional non-Hermitian Su–Schrieffer–Heeger lattice with periodic driving. The interplay between periodic driving and non-Hermiticity opens gaps at both zero and π quasienergies and gives rise to stable topological zero and π modes under open boundary conditions. To characterize the critical properties of the transition, we construct the fidelity susceptibility based on Floquet eigenstates and systematically compare two definitions: the self-normal fidelity and biorthogonal fidelity. In contrast to the self-normal fidelity susceptibility, the biorthogonal fidelity susceptibility exhibits a clear power-law scaling with system size and converges more reliably to the analytically expected critical points in the thermodynamic limit. Our results demonstrate that the biorthogonal fidelity susceptibility provides a robust and accurate approach to identifying Floquet non-Hermitian topological phase transitions and their quantum critical properties.