Dynamics of decoherence: universal scaling of the decoherence factor

Abstract

We study the time dependence of the decoherence factor (DF) of a qubit globally coupled to an environmental spin system (ESS) which is driven across the quantum critical point (QCP) by varying a parameter of its Hamiltonian in time $t$ as $1-t/\tau$ or $-t/\tau$, to which the qubit is coupled starting at the time $t\to -\infty$; here, $\tau$ denotes the inverse quenching rate. In the limit of weak coupling, we analyze the time evolution of the DF in the vicinity of the QCP (chosen to be at $t=0$) and define three quantities, namely, the generalized fidelity susceptibility ${\chi }_F(\tau )$ (defined right at the QCP), and the decay constants ${\alpha }_1(\tau )$ and ${\alpha }_2(\tau )$ which dictate the decay of the DF at a small but finite $t$($>0$). Using a dimensional analysis argument based on the Kibble-Zurek healing length, we show that ${\chi }_F(\tau )$ as well as ${\alpha }_1(\tau )$ and ${\alpha }_2(\tau )$ indeed satisfy universal power-law scaling relations with $\tau$ and the exponents are solely determined by the spatial dimensionality of the ESS and the exponents associated with its QCP. Remarkably, using the numerical t-DMRG method, these scaling relations are shown to be valid in both the situations when the ESS is integrable and non-integrable and also for both linear and non-linear variation of the parameter. Furthermore, when an integrable ESS is quenched far away from the QCP, there is a predominant Gaussian decay of the DF with a decay constant which also satisfies a universal scaling relation.

4 pages, 4 figures, 6 pages supplementary material

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• Finite temperature dynamical quantum phase transition in a non-Hermitian system
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• Dynamics of decoherence in a noisy driven environment
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• Entanglement entropy of a three-spin interacting spin chain with a time-reversal breaking impurity at one boundary
• Stacked quantum Ising systems and quantum Ashkin-Teller model
• Generation of concurrence in a generalized central spin model with a three-spin interacting environment
• Quantum many-body spin rings coupled to ancillary spins: The sunburst quantum Ising model