Abstract
We study the mixed state entanglement in a holographic axion model. We find that the holographic entanglement entropy (HEE), mutual information (MI) and entanglement of purification (EoP) exhibit very distinct behaviors with system parameters. The HEE exhibits universal monotonic behavior with system parameters, while the behaviors of MI and EoP relate to the specific system parameters and configurations. We find that MI and EoP can characterize mixed state entanglement better than HEE since they are less affected by thermal effects. Specifically, the MI partly cancels out the thermal entropy contribution, while the holographic EoP is not dictated by the thermal entropy in any situation. Moreover, we argue that EoP is more suitable for describing mixed state entanglement than MI. Because the MI of large configurations are still dictated by the thermal entropy, while the EoP will never be controlled only by the thermal effects.
Highlights
We study the properties of holographic entanglement entropy (HEE), mutual information (MI) and entanglement of purification (EoP), in a holographic axion model
When the size of the subregion is small, the minimum surface will approach the horizon of the black brane, so that the HEE will be mainly contributed by the thermal entropy
The MI behavior with k and T originates from the HEE that is dictated by thermal entropy, following the analysis given in Sect. 3.2.2, we see that the MI may still be determined by thermal effects
Summary
Where V (X ) is the kinematic term for the axion fields. The ψ I represents the linear axion field with a constant linear factor k. The regularity of the Maxwell field on the horizon requires that At |rh = 0, i.e., ρ = μrh. The linear axion fields break the translational symmetry, so the system has finite DC conductivity, which reads [38], σDC. We focus on the V (X ) = X 2 case, which goes back to [43]. We have examined the cases for V (X ) = X, X 3, X 4, X 5, numerically the phenomena we revealed in this paper are the same as that of V (X ) = X 2. We focus on scaling-invariant physical quantities, so we adopt μ as the scaling unit by setting μ = 1.
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