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We study the decoherence of a coupled quantum system consisting of a centralspin and its correlated environment described by a general $XY$ spin-chainmodel. We make it clear that the evolution of the coherence factor sensitivelydepends on the initial states of the environment spin-chain. Specially, thedynamical evolution of the coherence factor of the central spin is numericallyand analytically investigated in both weak and strong coupling cases fordifferent initial states including thermal equilibrium state. In both weak andstrong coupling regimes, the decay of the coherence factor can be approximatedby a Gaussian and in the strong coupling regime the coherence factor oscillaterapidly under a Gaussian envelope. The width of the Gaussian decay (envelope)has been studied in details and we explained the origin of the so-calleduniversal regime.

Decoherence of a quantum system coupled to an XY spin chain: Role of the initial state of the spin chain