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The transverse field in the quantum Ising chain is linearly ramped from thepara- to the ferromagnetic phase across the quantum critical point at a ratecharacterized by a quench time $\tau_Q$. We calculate a connected kink-kinkcorrelator in the final state at zero transverse field. The correlator is a sumof two terms: a negative (anti-bunching) Gaussian that depends on theKibble-Zurek (KZ) correlation length only and a positive term that depends on asecond longer scale of length. The second length is made longer by dephasing ofthe state excited near the critical point during the following ramp across theferromagnetic phase. This interpretation is corroborated by considering alinear ramp that is halted in the ferromagnetic phase for a finite waiting timeand then continued at the same rate as before the halt. The extra timeavailable for dephasing increases the second scale of length thatasymptotically grows linearly with the waiting time. The dephasing alsosuppresses magnitude of the second term making it negligible for waiting timesmuch longer than $\tau_Q$. The same dephasing can be obtained with a smoothramp that slows down in the ferromagnetic phase. Assuming sufficient dephasingwe obtain also higher order kink correlators and the ferromagnetic correlationfunction.

Quantum Kibble-Zurek mechanism: Kink correlations after a quench in the quantum Ising chain