Quantum speed limit for a central system in Lipkin-Meshkov-Glick bath

H. T. Quan, Z. D. Wang, C. P. Sun

We explore a dynamic signature of quantum phase transition (QPT) in an isotropic Lipkin-Meshkov-Glick (LMG) model by studying the time evolution of a central qubit coupled to it. We evaluate exactly the time-dependent purity, which can be used to measure quantum coherence, of the central qubit. It is found that distinctly different behaviors of the purity as a function of the parameter reveal clearly the QPT point in the system. It is also clarified that the present model is equivalent to an anti--Jaynes-Cummings model under certain conditions.

Wen-Jian Yu, Yong-Bo Wei, Hai Li +3 more

Lin Zhang, Yuan Sun, Shunlong Luo

Yamen Hamdouni

The dynamics of a central qubit system coupled to an isotropic ferromagnetic Lipkin–Meshkov–Glick spin bath at nonzero temperature is studied. We derive exactly the reduced density matrix and investigate the pairwise thermal entanglement, the coherence and the concurrence of the central spins. Through the behavior of these quantities, we show that at very low temperatures the dynamics is sensitive to the presence of the critical point of the environment.

Xue-Bing Wang, Wei Wu

Li-Ping Han, Jian Zou, Hai Li +1 more

Based on conditional past-future (CPF) correlations, we study the non-Markovianity of a central spin coupled to an isotropic Lipkin-Meshkov-Glick (LMG) bath. Although the dynamics of a system is always non-Markovian, it is found that some measurement time intervals considering a specific process, with respect to a particular set of CPF measurement operators, can be zero, which means that in this case the non-Markovianity of the system could not be detected. Furthermore, the initial system-bath correlations only slightly influence the non-Markovianity of the system in our model. Significantly, it is also found that the dynamics of the system for LMG baths, initially in the ground states corresponding to the symmetric phase and symmetry broken phase, exhibit different properties, and the maximal value of the CPF at the critical point is the smallest, independent of the measurement operator, which means that the criticality can manifest itself by the CPF. Moreover, the effect of bath temperature on the quantum criticality of the CPF depends on the measurement operator.