For algebraic quenches in the 1D TFIM, the longitudinal kink-kink correlator depends only on the KZ length for superlinear cases and otherwise needs a dephasing length, decaying as a compressed exponential with exponent varying continuously with the quench exponent.
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Kink-kink correlations in nonlinear quenches across a quantum critical point
For algebraic quenches in the 1D TFIM, the longitudinal kink-kink correlator depends only on the KZ length for superlinear cases and otherwise needs a dephasing length, decaying as a compressed exponential with exponent varying continuously with the quench exponent.