Abstract
We study the entanglement wedge cross-section (EWCS) in holographic massive gravity theory, in which a first and second-order phase transition can occur. We find that the mixed state entanglement measures, the EWCS and mutual information (MI) can characterize the phase transitions. The EWCS and MI show exactly the opposite behavior in the critical region, which suggests that the EWCS captures distinct degrees of freedom from that of the MI. More importantly, EWCS, MI and HEE all show the same scaling behavior in the critical region. We give an analytical understanding of this phenomenon. By comparing the quantum information behavior in the thermodynamic phase transition of holographic superconductors, we analyze the relationship and difference between them and provide two mechanisms of quantum information scaling behavior in the thermodynamic phase transition.
Highlights
JHEP08(2021)113 to the area of the minimum cosmic brane [24]
The patterns of characterizing the phase transition for HEE, mutual information (MI) and entanglement wedge cross-section (EWCS) are essentially the same: they encounter a jump at the first-order phase transition point and exhibit a singular behavior at the secondorder phase transition point
We observe an intriguing phenomenon that MI behavior with temperature is completely the opposite of that of the EWCS in the critical region
Summary
Where Gn is the n-dimensional Newton constant which we set as 1, fμν is the reference metric, 2) × (n ci are constants + 2) matrix Kμν and√ Ui are symmetric ≡ gμαfαν , polynomials of the eigenvalue of the M introduces mass to the graviton, which breaks the translational symmetry. We can denote the case of spherical, Ricci flat and hyperbolic horizon as k = 1, 0, −1. The first-order phase transition (β > 3Q) occurs when the entropy density jumps. The second-order phase transition (β = 3Q) occurs when the entropy density is continuous while its first derivative to temperature is discontinuous. Near the critical point β = 3Q where second-order phase transition occurs, as can be seen from figure 1, there is s (T ) → ∞. This suggests that a critical scaling behavior will emerge in the critical region. Similar analysis can be found in [68]
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