Holographic entanglement entropy from 2d CFT: heavy states and local quenches

By Curtis T Asplund, A. Bernamonti, F. Galli, Thomas Hartman. 2014

305 citations recorded by the source corpus.

A bstractWe consider the entanglement entropy in 2d conformal field theory in a class of excited states produced by the insertion of a heavy local operator. These include both high-energy eigenstates of the Hamiltonian and time-dependent local quenches. We compute the universal contribution from the stress tensor to the single interval Renyi entropies and entanglement entropy, and conjecture that this dominates the answer in theories with a large central charge and a sparse spectrum of low-dimension operators. The resulting entanglement entropies agree precisely with holographic calculations in three-dimensional gravity. High-energy eigenstates are dual to microstates of the BTZ black hole, so the corresponding holographic calculation is a geodesic length in the black hole geometry; agreement between these two answers demonstrates that these individual microstates of holographic CFTs effectively thermalize at the level of the single-interval entanglement entropy. For local quenches, the dual geometry is a highly boosted black hole or conical defect. On the CFT side, the rise in entanglement entropy after a quench is directly related to the monodromy of a Virasoro conformal block.

Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/9eebab0d4f9635a9f01451394039e7e961ed58fa

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Citations in the corpus

Bounding the space of holographic CFTs with chaos (2016, methodology): “(And even in this regime, the vacuum dominance of the correlator is believed to hold [64].”
Virasoro conformal blocks and thermality from classical background fields (2015, unknown): “The choice of branch cut in the logarithm determines how many times the geodesic winds [37] around the singularity.”
Witten diagrams revisited: the AdS geometry of conformal blocks (2015, result): “The ideas developed in this paper originated by thinking about the bulk representation of Virasoro conformal blocks in AdS3/CFT2, based on recent results in this direction [28–33].”
Causality constraints in conformal field theory (2015, methodology): “A similar approach has been applied to entanglement entropy [42, 43] and correlation functions of primary operators [18, 25, 43] using conformal bootstrap methods very similar to those deployed in this paper.”
Entanglement scaling of operators: a conformal field theory approach, with a glimpse of simulability of long-time dynamics in 1 + 1d (2016, methodology): “(a) The regularization scheme (adapted from [89, 90]) in our tentative CFT calculation of the OSEE of some generic operator φ(t): we calculate a four-point function of the form 〈 φ†T †φT 〉 on the cylinder of circumference βv, and then take the analytic continuation y → ivt , and |x|, vt βv.”
Virasoro conformal blocks in closed form (2015, background): “4) or as a geodesic length in an asymptotically AdS3 geometry [39, 40].”
Chaos in quantum channels (2015, background): “For holographic systems, this is known not to happen: after SFG saturates, it remains saturated [58, 59, 60, 32, 61].”
Black hole collapse in the 1/c expansion (2016, methodology): “Now the leading contribution to the Rényi entropy near n = 1 comes from the heavy-heavy-lightlight four-point function 〈Oσnσ̃nO〉, which was computed in [30], suitably continued to reproduce the Lorentzian orderings in (A.”