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

We study the decoherence of a coupled quantum system consisting of a central spin and its correlated environment described by a general $XY$ spin-chain model. We make it clear that the evolution of the coherence factor sensitively depends on the initial states of the environment spin-chain. Specially, the dynamical evolution of the coherence factor of the central spin is numerically and analytically investigated in both weak and strong coupling cases for different initial states including thermal equilibrium state. In both weak and strong coupling regimes, the decay of the coherence factor can be approximated by a Gaussian and in the strong coupling regime the coherence factor oscillate rapidly under a Gaussian envelope. The width of the Gaussian decay (envelope) has been studied in details and we explained the origin of the so-called universal regime.