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

TL;DR

This paper establishes a relationship between non-Markovianity measures and the Loschmidt echo in a qubit-environment system, showing that non-Markovianity signals environmental criticality, especially in quantum phase transitions.

Contribution

It introduces a unified framework linking non-Markovianity and Loschmidt echo, demonstrating how environmental criticality influences system dynamics and non-Markovian behavior.

Findings

Loschmidt echo relates to information flow in the system.

Non-Markovianity peaks away from the critical point.

Criticality induces Markovian dynamics at the transition.

Abstract

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