Remarks on the entanglement entropy for disconnected regions
225 citations recorded by the source corpus.
Few facts are known about the entanglement entropy for disconnected regions in quantum field theory. We study here the property of extensivity of the mutual information, which holds for free massless fermions in two dimensions. We uncover the structure of the entropy function in the extensive case, and find an interesting connection with the renormalization group irreversibility. The solution is a function on space-time regions which complies with all the known requirements a relativistic entropy function has to satisfy. We show that the holographic ansatz of Ryu and Takayanagi, the free scalar and Dirac fields in dimensions greater than two, and the massive free fields in two dimensions all fail to be exactly extensive, disproving recent conjectures.
Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/643075b3cb5a13411dc13e0bf031bff66266c18b
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In Atomic and Molecular Physics, and Optics
In Nuclear and High Energy Physics
Citations in the corpus
- Entanglement entropy from a holographic viewpoint (2012, background): “For relevant calculations in the CFT side refer to [100–103].”
- Mutual information and the F-theorem (2015, methodology): “Appendix C presents calculations of mutual information in a particular model where the mutual information satisfies a certain extensivity property [47].”
- Deriving covariant holographic entanglement (2016, background): “Since ρA is a wedge observable [18] (see also [12]), it cannot depend on which Cauchy slice we pick in the domain of dependence of the chosen region D[A].”
- Quantum corrections to holographic entanglement entropy (2013, background): “As discussed in [30,34–36], the expected leading contribution comes from the exchange of a pair of operators each with dimension ∆ .”
- Holographic entanglement entropy: an overview (2009, background): “40,108,109] as it essentially becomes products of two point functions of twisted vertex operators. In the case where the subsystem Aconsists of multiple intervals, recent discussions are available in [74,110,111]. However, in higher dimensions, analytical calculations of SA become very complicated. ”
- Entanglement entropy of two disjoint intervals in conformal field theory (2009, methodology): “[24, 25, 26, 27], the entanglement entropy for two disjoint intervals has been calculated for a free massless Dirac fermion, that corresponds to a compactified boson with η = 1/2 [12].”
- Towards a derivation of holographic entanglement entropy (2011, methodology): “A regularization of the entanglement entropy implementing a distance cutoff to the entangling sphere can be made precise using the mutual information [28].”
- Holographic mutual information is monogamous (2011, methodology): “14) applies only to CFTs, so is not in conflict with the results of [7] for massive fermions.”