Decoherence induced by a dynamic spin environment (I): The universal regime

This article analyzes the decoherence induced on a single qubit by the interaction with a spin chain with nontrivial internal dynamics (XY-type interactions). The aim of the paper is to study the existence and properties of the so-called universal regime, in which the decoherence time scale becomes independent of the strength of the coupling with the environment. It is shown that although such regime does exist, as previously established by Cucchietti \textit{et al} in {\em Phys. Rev. A}, 75:032337 (2007), it is not a clear signature of a quantum phase transition in the environment. In fact, this kind of universality also exists in the absence of quantum phase transitions. A universal regime can be related to the existence of an energy scale separation between the Hamiltonian of the environment and the one characterizing the system-environment interaction. The results presented also indicate that in the strong coupling regime the quantum phase transition does not produce an enhancement of decoherence (as opposed to what happens in the weak coupling regime).