Steady-state susceptibility in continuous phase transitions of dissipative systems

In this work we explore the critical behaviors of fidelity susceptibility and trace distance susceptibility associated with the steady states of dissipative systems at continuous phase transitions. We investigate two typical models: One is the dissipative spin-1/2 XYZ model on a two-dimensional square lattice and the other is a driven-dissipative Kerr oscillator. We find that the susceptibilities of fidelity and trace distance exhibit singular behaviors near the critical points of phase transitions in both models. The critical points in the thermodynamic limit, extracted from the scalings of the critical controlling parameters to the system size or nonlinearity, agree well with the existing results.