Entanglement entropy of two disjoint intervals in conformal field theory: II
By Pasquale Calabrese, J. Cardy, E. Tonni. 2010
283 citations recorded by the source corpus.
We continue the study of the entanglement entropy of two disjoint intervals in conformal field theories that we started in Calabrese et al 2009 J. Stat. Mech. P11001. We compute TrρAn for any integer n for the Ising universality class and the final result is expressed as a sum of Riemann–Siegel theta functions. These predictions are checked against existing numerical data. We provide a systematic method that gives the full asymptotic expansion of the scaling function for small four-point ratio (i.e. short intervals). These formulas are compared with the direct expansion of the full results for a free compactified boson and Ising model. We finally provide the analytic continuation of the first term in this expansion in a completely analytic form.
Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/98a73cd690573467679d1225c44d6c29d76c0a68
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Citations in the corpus
- Entanglement negativity in extended systems: a field theoretical approach (2012, methodology): “It is also worth reporting the first terms in the short length expansion (76) in the case of a compactified free boson [35]”
- Virasoro conformal blocks in closed form (2015, background): “Away from the entanglement entropy limit n → 1, and the case n = 2 (for which S2 is the free energy of the CFT on a torus), Sn has only been computed in a short interval expansion, z ≪ 1 [31, 32].”
- Holographic entanglement beyond classical gravity (2013, methodology): “It is known, however, that there are universal terms that must appear in the entanglement entropy that depend on the distance between the two intervals [9, 10].”
- Holographic calculations of Rényi entropy (2011, methodology): “Even in two dimensions, if we consider two separate intervals calculating the Rényi entropy requires detailed information about the full spectrum of the corresponding CFT [51].”
- Entanglement entropy and conformal field theory (2009, methodology): “However, it has been found that the entanglement entropy is given by Z Rn,2 , in contrast with the numerical calculations in [71] and the analytic one in [74].”
- Entanglement Entropy at Large Central Charge (2013, background): “The entanglement entropy of a subsystem that consists of multiple disjoint intervals depends, in general, on the full operator content of the theory [4, 5].”
- Unusual corrections to scaling in entanglement entropy (2010, methodology): “In fact, to build the reduced density of the spin degrees of freedom in the Ising model, one should introduce the non local Jordan-Wigner string between the two intervals [43, 42, 44], that plays the rule of the Ising fermion.”
- Holographic evolution of the mutual information (2011, methodology): “Interesting insights in the structure of entanglement can be obtained by considering two disjoint regions, namely A = A1 ∪ A2 with A1 ∩ A2 = ∅ [15, 16, 17, 18].”
- Holographic mutual information is monogamous (2011, background): “(2.8) Calabrese, Cardy, and Tonni [17] computed the leading behavior of the mutual information for small x (i.e. large separation relative to the sizes of the intervals) in a general CFT”