Abstract
We use the AdS/CFT correspondence to study models of entanglement and correlations between two $d=4$ CFTs in thermofield double states at finite chemical potential. Our bulk spacetimes are planar Reissner-Nordstr\"om AdS black holes. We compute both thermo-mutual information and the two-point correlators of large-dimension scalar operators, focussing on the small-temperature behavior -- an infrared limit with behavior similar to that seen at large times. The interesting feature of this model is of course that the entropy density remains finite as $T \rightarrow 0$ while the bulk geometry develops an infinite throat. This leads to a logarithmic divergence in the scale required for non-zero mutual information between equal-sized strips in the two CFTs, though the mutual information between one entire CFT and a finite-sized strip in the other can remain non-zero even at $T=0$. Furthermore, despite the infinite throat, there can be extremally charged operators for which the two-point correlations remain finite as $T \rightarrow 0$. This suggests an interestingly mixed picture in which some aspects of the entanglement remain localized on scales set by the chemical potential, while others shift to larger and larger scales. We also comment on implications for the localized-quasiparticle picture of entanglement.
Highlights
We focus on the holographic setting below
Our bulk spacetimes are planar Reissner-Nordstrom AdS black holes. We compute both thermo-mutual information and the two-point correlators of large-dimension scalar operators, focussing on the small-temperature behavior — an infrared limit with behavior similar to that seen at large times
For simplicity we focus on TFD states which are holographically dual to planar Reissner-Nordstrom AdS (RNAdS)
Summary
Since any remaining entanglement is associated with excitations of vanishingly small energy above the ground state (in the sense of H1, H2), one might expect any spatial scale characterizing our TFD entanglement to diverge as T → 0. Since we consider RNAdS5, our bulk dual will have an AdS2 × R3 infrared fixed point describing the near-horizon region Such spacetimes exhibit local criticality, characterized by the limit z → ∞ of dynamical scaling symmetry (t, x) → (λzt, λx) which for finite z would give a power law L ∼ T −1/z.
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