Entanglement entropy of two disjoint intervals in conformal field theory

By Pasquale Calabrese, J. Cardy, E. Tonni. 2009

434 citations recorded by the source corpus.

We study the entanglement of two disjoint intervals in the conformal field theory of the Luttinger liquid (free compactified boson). Tr ρAn for any integer n is calculated as the four-point function of twist fields of a particular type and the final result is expressed in a compact form in terms of the Riemann–Siegel theta functions. In the decompactification limit we provide the analytic continuation valid for all model parameters and from this we extract the entanglement entropy. These predictions are checked against existing numerical data.

Subfields: Astronomy and Astrophysics, Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/396093ba3b626d52975b6276177079a5af01f1dd

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Citations in the corpus

Quantum corrections to holographic entanglement entropy (2013, background): “18) can be continued to n = 1 [35].”
Entanglement entropy of two disjoint intervals in conformal field theory: II (2010, methodology): “In [1] we have used that Θ(0|A−1ΓA) = Θ(0|Γ) without proof (see equation (B.”
The Entanglement Renyi Entropies of Disjoint Intervals in AdS/CFT (2013, background): “The focus of this paper will be 1+1 CFTs where the sub-region of interest A is the union of a set of intervals along the spatial axis [10, 21] and we consider only the vacuum state of the CFT.”
A stereoscopic look into the bulk (2016, neutral): “Related formulations have been explored in [42–44].”
A general proof of the quantum null energy condition (2017, background): “These operators are important when replacing non-local twist operators with local operators when viewed from a distance, as in [77–81], or when bringing a twist operator close to an anti-twist operator, as in [34, 82].”
Islands in cosmology (2020, positive): “3) z2 = rI − tI + iβ/4 z̄2 = rI + tI − iβ/4 z3 = −rR − tR − iβ/4 z̄3 = −rR + tR + iβ/4 z4 = rR − tR − iβ/4 z̄4 = rR + tR + iβ/4 We will calculate the Renyi partition function Zn = Tr (ρI∪R) n using the twist operator methods of Cardy and Calabrese [100, 101], as applied to this problem in [53] (see ”
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 [30, 31].”
Finite temperature entanglement negativity in conformal field theory (2014, methodology): “The correction to the zero temperature behaviour are more involved but they can be obtained as an application of the short-length expansion developed in [45], which requires to take into account the next order in the OPE (32).”
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 of two disjoint blocks in XY chains (2010, background): “This has been extended to general integer α ≥ 2 in [12]:”
Quantum quenches in 1 + 1 dimensional conformal field theories (2016, background): “The OPE of twist operators is expressed as a sum of products of local operators in each sheet as [56, 57]”
Entanglement negativity in extended systems: a field theoretical approach (2012, methodology): “In this case, the limit of equation (78) for η 1 has been worked out in [34] and it reads for 0 < x < 1”