Tripartite information at long distances

Abstract

We compute the leading term of the tripartite information at long distances for three spheres in a CFT. This falls as $r^{-6\Delta }$, where $r$ is the typical distance between the spheres, and $\Delta$, the lowest primary field dimension. The coefficient turns out to be a combination of terms coming from the two- and three-point functions and depends on the OPE coefficient of the field. We check the result with three-dimensional free scalars in the lattice finding excellent agreement. When the lowest-dimensional field is a scalar, we find that the mutual information can be monogamous only for quite large OPE coefficients, far away from a perturbative regime. When the lowest-dimensional primary is a fermion, we argue that the scaling must always be faster than $r^{-6{\Delta }_f}$. In particular, lattice calculations suggest a leading scaling $r^{-(6{\Delta }_f+1)}$. For free fermions in three dimensions, we show that mutual information is also non-monogamous in the long-distance regime.

25 pages and 5 figures. V2: References added, a paragraph with comments on $d=2$ results was included and it matches the version to appear in SciPost

References in corpus (11)

• Towards a derivation of holographic entanglement entropy
• Entanglement entropy of two disjoint intervals in conformal field theory II
• Entanglement entropy, conformal invariance and extrinsic geometry
• Remarks on the entanglement entropy for disconnected regions
• Critical $O(N)$ Models in $6-\epsilon$ Dimensions
• Entanglement entropy and negativity of disjoint intervals in CFT: Some numerical extrapolations
• Quantum Extremal Surfaces and the Holographic Entropy Cone
• Mutual information and the F-theorem
• Quantum bit threads and holographic entanglement
• Scattering strings off quantum extremal surfaces
• On co-dimension two defect operators

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• Entanglement negativity between separated regions in quantum critical systems
• A universal feature of charged entanglement entropy
• Negative tripartite mutual information after quantum quenches in integrable systems
• Universality in the tripartite information after global quenches
• Aspects of N-partite information in conformal field theories
• Universality in the tripartite information after global quenches: (generalised) quantum XY models
• Universality in the tripartite information after global quenches: spin flip and semilocal charges
• Mutual information from modular flow in CFTs
• Scrambling in Ising spin systems with periodic transverse magnetic fields