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We study the scaling of the decoherence factor of a qubit (spin-1/2) usingthe central spin model in which the central spin (qubit) is globally coupled toa transverse XY spin chain. The aim here is to study the non-equilibriumgeneration of decoherence when the spin chain is driven across (along) quantumcritical points (lines) and derive the scaling of the decoherence factor interms of the driving rate and some of the exponents associated with the quantumcritical points. Our studies show that the scaling of logarithm of decoherencefactor is identical to that of the defect density in the final state of thespin chain following a quench across isolated quantum critical points for bothlinear and non-linear variations of a parameter even if the defect density maynot satisfy the standard Kibble-Zurek scaling. However, one finds aninteresting deviation when the spin chain is driven along a critical line. Ouranalytical predictions are in complete agreement with numerical results. Ourstudy, though limited to integrable two-level systems, points to the existenceof a universality in the scaling of the decoherence factor which is notnecessarily identical to the scaling of the defect density.

The scaling of the decoherence factor of a qubit coupled to a spin chain driven across quantum critical points