Adiabatic transformations in dissipative and non-Hermitian phase transitions

The quantum geometric tensor has established itself as a general framework for the analysis and detection of equilibrium phase transitions in isolated quantum systems. We propose a generalization of the quantum geometric tensor, which offers a universal approach to studying phase transitions in non-Hermitian quantum systems. Our generalization is based on the concept of the generator of adiabatic transformations and can be applied to systems described by either a Liouvillian superoperator or by an effective non-Hermitian Hamiltonian. We illustrate the proposed method by analyzing the non-Hermitian Su-Schrieffer-Heeger model and a generic quasifree dissipative fermionic system with a quadratic Liouvillian. Our findings reveal that this method effectively identifies phase transitions across all examined models, providing a universal tool for investigating general non-Hermitian systems.