Mixed state entanglement and thermal phase transitions

We study the relationship between mixed state entanglement and thermal phase transitions. As a typical example, we compute holographic entropy (HEE), mutual information (MI) of purification (EoP) over superconductivity transition. find that HEE, MI EoP can all diagnose superconducting They are continuous at critical point, but their first derivative with respect to temperature is discontinuous. decreases increasing exhibits convex behavior, while HEE increases concave behavior. However, exhibit either same or opposite behavior as MI, depending on size specific configuration. These results show captures more abundant than MI. also provide new algorithm for general configurations.