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

Quantum criticality and the existence of long-range correlations in the ground state have been extensively studied, yet it remains unclear whether such features persist in the stationary state after a quench. Recent studies on the short-range anisotropic XY model[1]showed that, for critical-to-critical quenches, peaks in mutual information and logarithmic negativity indicate stationary-state criticality, arising from algebraically decaying fermionic correlators. In contrast, long-range systems can exhibit algebraic decay even away from criticality, raising questions about the existence of such peaks. To address this, we study a one-diemntional long-range Kitaev model with power-law pairing interactions. We find pronounced peaks in bipartite and tripartite mutual information and logarithmic negativity following a critical-to-critical quench [2]. These peaks do not arise from a change in form of correlator decay but from a discontinuity in the post-quench Bogoliubov quasiparticle occupation probabilities. The effective central charge, obtained from finite size scaling of both mutual information and logarithmic negativity in the stationary state following critical-to-critical quench, agrees with the central charge of the corresponding critical ground states for pairing exponent values $\alpha = 0$ and $\alpha = 2$, revealing that the universality class of the steady state can be inferred from the ground state.

[1] S. Paul, P. Titum, and M. Maghrebi, Phys. Rev. Research 6, L032003 (2024)