Sudden birth and sudden death of thermal fidelity in a two-qubit system

We study the energy level crossing and the thermal fidelity in a two-qubit system with the presence of a transverse inhomogeneous magnetic field. With the help of contour plots, we clearly identify the ground states of the system in different regions of parameter space, and discuss the corresponding energy level crossing. The fidelity between the ground state of the system and the state of the system at temperature T is calculated. The result shows that the fidelity is very sensitive to the magnetic field anisotropic factor, indicating that this factor may be used as a controller of the fidelity. The influence of the Yangian transition operators on the fidelity of the system is discussed. We find that the Yangian operators can change the fidelity dramatically and give rise to sudden birth and sudden death phenomena of the thermal fidelity. This makes the corresponding Yangian operators possible candidates for switchers to turn the fidelity on and off.