Mixed State Entanglement and Thermal Phase Transitions

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 of purification (EoP) over the superconductivity phase transition. We find that HEE, MI and EoP 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, EoP can exhibit either the same or the opposite behavior as MI, depending on the size of the specific configuration. These results show that EoP captures more abundant information than HEE and MI. We also provide a new algorithm to compute the EoP for general configurations.

24 pages, 13 figures, References added

References in corpus (13)

• Building an AdS/CFT superconductor
• Entanglement as a Probe of Confinement
• Deriving covariant holographic entanglement
• Introduction to Holographic Superconductor Models
• Holographic Entanglement Entropy in Insulator/Superconductor Transition
• Holographic Entanglement Entropy in P-wave Superconductor Phase Transition
• Note on the butterfly effect in holographic superconductor models
• Interplay between the holographic QCD phase diagram and mutual & $n$-partite information
• Holographic entanglement entropy close to crossover/phase transition in strongly coupled systems
• Informational properties for Einstein-Maxwell-Dilaton Gravity
• Informational properties of holographic Lifshitz field theory
• Entanglement measures for non-conformal D-branes
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Cited by in corpus (8)

• Mixed state entanglement measures as probe for confinement
• Holographic confining/deconfining gauge theories and entanglement measures with a magnetic field
• Informational properties of holographic Lifshitz field theory
• Entanglement Wedge Minimum Cross-Section for Holographic Aether Gravity
• Entanglement Wedge Cross Section with Gauss-Bonnet Corrections and Thermal Quench
• Mixed-state Entanglement for AdS Born-Infeld Theory
• Non-Conformal Behavior of Holographic Entanglement Measures
• More on entanglement properties of $Li{f}_4^{(2)}\times S^1\times S^5$ spacetime with string excitations