Quantum criticality and universality in stationary state of long-range Kitaev model

We investigate the signature of quantum criticality in the long-time stationary state of the long-range Kitaev chain by performing various quench protocols. In this model, the pairing interaction decays with distance according to a power law with exponent $\alpha$. Using quantum information-theoretic measures, such as mutual information and logarithmic negativity, we show that, irrespective of the values of $\alpha$, critical-to-critical quench displays quantum criticality even in the stationary state. Remarkably, in the presence of long-range pairing interactions, where fermionic correlators decay algebraically even at non-critical points, signature of quantum criticality persists in the stationary state. Furthermore, the effective central charge, calculated from both mutual information and logarithmic negativity of stationary state following a critical-to-critical quench, agrees with the central charge of the corresponding ground states for both $\alpha = 0$ and $\alpha = 2$. Therefore, information of the universality class can be inferred from the stationary state.