Decoherence of a central quantum system coupled to an XY spin chain

We investigate decoherence of a central quantum system uniformly coupled to an XY spin-1/2 bath in a transverse field. Through explicitly calculating the Loschmidt echo ( LE) used to characterize decoherence quantitatively we find that the anisotropy parameter gamma sensitively affects the decoherence of the central system when gamma is an element of [ 0, 1]. Interestingly, the LE becomes unit under the condition that the initial state of the environment is a product state. Although it is difficult to control the environment to be product states in reality, our findings may provide a new understanding of mechanism of the decoherence.