Sudden transition and sudden change from open spin environments

•Sudden transition or sudden change from open spin baths are studied.•Quantum discord is related to the Loschmidt echo in independent open spin baths.•Steady quantum discord is found in a common open spin bath.•The probability distribution of the Loschmidt echo is analyzed.•The scaling transformation behavior of quantum discord is displayed.

We investigate the necessary conditions for the existence of sudden transition or sudden change phenomenon for appropriate initial states under dephasing. As illustrative examples, we study the behaviors of quantum correlation dynamics of two noninteracting qubits in independent and common open spin environments, respectively. For the independent environments case, we find that the quantum correlation dynamics is closely related to the Loschmidt echo and the dynamics exhibits a sudden transition from classical to quantum correlation decay. It is also shown that the sudden change phenomenon may occur for the common environment case and stationary quantum discord is found at the high temperature region of the environment. Finally, we investigate the quantum criticality of the open spin environment by exploring the probability distribution of the Loschmidt echo and the scaling transformation behavior of quantum discord, respectively.