Kink correlations, domain-size distribution, and emptiness formation probability after a Kibble-Zurek quench in the quantum Ising chain

Linear quench of the transverse field drives quantum Ising chain across a critical point from paramagnetic to ferromagnetic phase. We focus on normal and anomalous quadratic correlators between fermionic kink creation annihilation operators. They depend not only Kibble-Zurek (KZ) correlation length but also dephasing scale, which differs KZ by logarithmic correction. Additional slowing down ramp in phase further increases suppresses correlator. The enter Pfaffians that yield experimentally relevant functions, probability distribution domain sizes, and, closely related, emptiness formation probability. latter takes form Pfaffian block Toeplitz matrix allows for some analytic asymptotes. Finally, we obtain insight into structure state at end interpreting it as paired kinks characterized its pair wave function. All those quantities are sensitive coherence eigenstates with different numbers kinks, thus making them convenient probe quantumness simulator platform.