Tanay Nag, Uma Divakaran, Amit Dutta
In this paper, we study the scaling of the decoherence factor of a qubit (spin-1/2) using the central spin model in which the central spin (qubit) is globally coupled to a transverse XY spin chain. The aim here is to study the non-equilibrium generation of decoherence when the spin chain is driven across quantum critical points (or lines) and derive the scaling of the decoherence factor in terms of the driving rate and some of the exponents associated with the quantum critical points. Our studies show that the scaling of logarithm of decoherence is identical to that of the defect density in the final state of the spin chain following a quench across isolated quantum critical points for both linear and non-linear variations of a parameter even if the defect density may not satisfy the standard Kibble-Zurek scaling. However, one finds an interesting deviation when the spin chain is driven along a critical line which is not given by the scaling of the defect density. Our analytical results, obtained via the exact solution of the Schr\"odinger equations as well as using an alternative method of calculating the Loschmidt echo are in complete agreement with numerical results.
View original:
http://arxiv.org/abs/1203.1186
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