Non-Markovianity, Loschmidt echo, and criticality: A unified picture

摘要

A simple relationship between recently proposed measures of non-Markovianity and the Loschmidt echo isnestablished, holding for a two-level system (qubit) undergoing pure dephasing due to a couplingwith amany-bodynenvironment. We show that the Loschmidt echo is intimately related to the information flowing out from andnoccasionally back into the system. This, in turn, determines the non-Markovianity of the reduced dynamics. Innparticular, we consider a central qubit coupled to a quantum Ising ring in the transverse field. In this context,nthe information flux between system and environment is strongly affected by the environmental criticality; thenqubit dynamics is shown to be Markovian exactly and only at the critical point. Therefore, non-Markovianity isnan indicator of criticality in the model considered here.