Decoherence by a quantum critical environment

We study the transition of a quantum system $S $ from a pure state to a mixed one, which is induced by the quantum criticality of the surrounding system $E$ coupled to it. To characterize this transition quantitatively, we carefully examine the behavior of the Loschmidt echo (LE) of $E$ modelled as an Ising model in a transverse field, which behaves as a measuring apparatus in quantum measurement. It is found that the quantum critical behavior of $E$ strongly affects its capability of enhancing the decay of LE: near the critical value of the transverse field entailing the happening of quantum phase transition, the off-diagonal elements of the reduced density matrix describing $S$ vanish sharply.