Non-Markovianity of a qubit coupled with an isotropic Lipkin–Meshkov–Glick bath

We study the non-Markovianity of the single qubit system coupled with an isotropic Lipkin–Meshkov–Glick(LMG)model by an effective method proposed by Breuer et al.(Breuer H P and Piilo J 2009 Europhys. Lett. 85 5004). It is discovered that the non-Markovianity is concerned with the quantum phase transitions(QPTs). In the open system, we present that the strong coupling inside the bath and the strong interaction between the system and bath can enhance the degree of non-Markovianity. Moreover, the non-Markovianity is stronger and more sensitive for the bath in the symmetric phase than the symmetry broken phase.