Abstract
We study the relationship between mixed state entanglement and thermal phase transitions. As a typical example, we compute the holographic entanglement entropy (HEE), holographic mutual information (MI), and the holographic entanglement wedge minimum cross section (EWCS) over the superconductivity phase transition. We find that HEE, MI, and EWCS can all diagnose the superconducting phase transition. They are continuous at the critical point, but their first derivative with respect to temperature is discontinuous. MI decreases with increasing temperature and exhibits a convex behavior, while HEE increases with increasing temperature and exhibits a concave behavior. However, EWCS can exhibit either the same or the opposite behavior as MI, depending on the size of the specific configuration. These results show that EWCS captures more abundant information than HEE and MI. We also provide a new algorithm to compute the EWCS for general configurations.
Highlights
Quantum entanglement is the main property that distinguishes quantum systems from classical systems
We find that holographic entanglement entropy (HEE), mutual information (MI), and entanglement wedge minimum cross section (EWCS) can all diagnose the superconducting phase transition
MI decreases with increasing temperature and exhibits a convex behavior, while HEE increases with increasing temperature and exhibits a concave behavior
Summary
Quantum entanglement is the main property that distinguishes quantum systems from classical systems. The entanglement wedge minimum cross section (EWCS) has been considered the holographic dual of some other mixed state entanglement measure, such as logarithmic negativity, reflected entropy and odd entropy [45,46,47]. HEE has been widely studied over many different holographic phase transition models, but the research on mixed state entanglement—MI and EWCS, are still missing. For this purpose, we study the properties. We focus on the relationship between these information-related physical quantities and phase transitions and pay special attention to the difference and relationship between mixed state entanglement measures and HEE.
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