pith. machine review for the scientific record. sign in

arxiv: 2604.26600 · v1 · submitted 2026-04-29 · ✦ hep-th

Recognition: unknown

Entanglement Revivals and Scrambling for Evaporating Black Holes

Levy B. N. Batista, Nicol\`o Bragagnolo, Rhys Holmes, S. Prem Kumar

Authors on Pith no claims yet

Pith reviewed 2026-05-07 10:38 UTC · model grok-4.3

classification ✦ hep-th
keywords entanglement revivalsblack hole scramblingevaporating black holesJT gravityRST modelmutual informationisland purification2d CFT
0
0 comments X

The pith

Increasing black hole scrambling time suppresses and eventually eliminates late-time entanglement spikes between disjoint intervals in evaporating black holes.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper studies entanglement spreading in free fermion conformal field theory on evaporating black hole backgrounds in two-dimensional gravity. It shows that ramping up the black hole scrambling time smooths out and removes late-time spikes in mutual information for separated intervals, which normally come from island-induced purification. This effect appears in both Jackiw-Teitelboim gravity and the Russo-Susskind-Thorlacius model, bridging quasiparticle pictures with maximal scrambling. At a critical scrambling strength the spikes vanish and the required interval lengths grow exponentially with scrambling time. The work also identifies a related entanglement dip for a single interval in a single-sided evaporating black hole.

Core claim

In Jackiw-Teitelboim gravity and the Russo-Susskind-Thorlacius model, parametrically increasing black hole scrambling time suppresses entanglement spikes in mutual information for disjoint intervals in the thermofield double state until they disappear at a critical scale where interval lengths are exponential in the scrambling time. This interpolates between free quasiparticle and maximal scrambling behaviors, with a related entanglement dip observed in single-sided evaporating RST black holes.

What carries the argument

Island-induced purification of modes in the union of intervals, controlled by black hole scrambling time in JT and RST evaporating geometries, which damps late-time mutual information revivals.

If this is right

  • Entanglement revivals are completely eliminated once scrambling time reaches the critical value.
  • The transition connects the quasiparticle regime to the maximal-scrambling regime in a controlled way.
  • A similar suppression appears as an entanglement dip for single intervals in single-sided RST black holes.
  • The critical interval length scales exponentially with black hole scrambling time in both models.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Stronger scrambling may help protect information from premature leakage during black hole evaporation.
  • The exponential scale at criticality could link to decoding protocols or information recovery in chaotic systems.
  • Extending the calculation to interacting CFTs or higher-dimensional black holes would test whether the suppression persists beyond free fermions.
  • The effect suggests a tunable knob for studying the crossover between ballistic and chaotic entanglement dynamics in curved spacetime.

Load-bearing premise

The free fermion CFT in thermofield double state on these specific 2d evaporating backgrounds accurately captures the island-induced purification mechanism without higher-order corrections or backreaction effects that would alter the scrambling-entanglement interplay.

What would settle it

A calculation of mutual information in either the JT or RST model at large scrambling time that still exhibits spikes for intervals shorter than exponential in the scrambling time would falsify the suppression and disappearance at criticality.

read the original abstract

We investigate the spreading of entanglement, and entanglement memory effects, in two dimensional conformal field theory (CFT) propagating on evaporating black hole backgrounds. Memory effects leading to late-time spikes in mutual information for widely separated intervals are well known in CFTs admitting a quasiparticle description. In this work we examine the effect of black hole scrambling on late time mutual information spikes for disjoint intervals in free fermion CFT prepared in a thermofield double state. Late-time entanglement revival is driven by island-induced purification of modes in the union of the intervals. We show across two distinct 2d gravity models, Jackiw-Teitelboim (JT) gravity and the Russo-Susskind-Thorlacius (RST) model, that parametrically dialing up black hole scrambling time smooths out and suppresses entanglement spikes until they disappear at a critical scale, interpolating between free quasiparticle and maximal scrambling pictures. At the critical point, the interval lengths are exponential in black hole scrambling time. We further find a very closely related effect manifest as an entanglement dip for a single interval in a single-sided evaporating RST black hole.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript examines entanglement revivals and memory effects in free fermion CFT on evaporating black hole spacetimes in two 2d gravity models: JT gravity and the RST model. It claims that increasing the black hole scrambling time parametrically suppresses late-time spikes in mutual information for disjoint intervals, with the spikes disappearing at a critical scrambling time scale where the interval lengths become exponential in the scrambling time. This interpolates between quasiparticle and maximal scrambling regimes. Additionally, an entanglement dip is reported for a single interval in the single-sided RST black hole.

Significance. If the central results hold, this work provides a concrete demonstration of how black hole scrambling influences entanglement dynamics in evaporating geometries, offering a bridge between quasiparticle pictures and strong scrambling limits. The exponential relation at criticality is a sharp prediction that could be tested in other models or via holographic calculations. The use of two distinct models strengthens the claim.

major comments (2)
  1. [Abstract and §3] Abstract and §3: The central results on suppression of mutual information spikes and the exponential scaling at criticality are stated without explicit derivations, error estimates, or numerical checks. The full calculations for the mutual information in the two models are not detailed enough to verify the claimed behavior when scrambling time is dialed up parametrically. This is load-bearing for the interpolation claim.
  2. [§2 (Model Setup)] §2 (Model Setup): The assumption that the free-fermion CFT in the thermofield double state on the time-dependent evaporating background accurately captures island-induced purification without higher-order gravitational corrections or CFT interactions is not justified when the scrambling time becomes parametrically large. Such corrections could modify the effective transmission of information across the island and alter the suppression of spikes and the critical exponential relation.
minor comments (1)
  1. [Figures] Figure captions and axis labels could more explicitly indicate the values of scrambling time and the location of the critical scale to aid readability of the suppression effect.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading, positive assessment of the work's significance, and constructive comments. We have revised the manuscript to address the concerns about explicit derivations and model justifications. Our point-by-point responses follow.

read point-by-point responses

  1. Referee: [Abstract and §3] Abstract and §3: The central results on suppression of mutual information spikes and the exponential scaling at criticality are stated without explicit derivations, error estimates, or numerical checks. The full calculations for the mutual information in the two models are not detailed enough to verify the claimed behavior when scrambling time is dialed up parametrically. This is load-bearing for the interpolation claim.

    Authors: We agree that the original presentation summarized the results too concisely. In the revised version, §3 now contains explicit step-by-step derivations of the mutual information for both JT and RST models using the replica trick combined with the island formula. We derive the late-time spike suppression analytically and obtain the exponential scaling at criticality in the large-scrambling-time limit. A new appendix provides the full expressions, numerical checks with error estimates from finite-size and discretization effects, and plots showing the progressive smoothing of spikes as the scrambling time is increased parametrically. These additions make the claimed interpolation between quasiparticle and maximal-scrambling regimes verifiable. revision: yes

  2. Referee: §2 (Model Setup): The assumption that the free-fermion CFT in the thermofield double state on the time-dependent evaporating background accurately captures island-induced purification without higher-order gravitational corrections or CFT interactions is not justified when the scrambling time becomes parametrically large. Such corrections could modify the effective transmission of information across the island and alter the suppression of spikes and the critical exponential relation.

    Authors: This is a legitimate concern. We have expanded §2 with a new paragraph justifying the regime of validity. The free-fermion CFT in the TFD state is chosen to permit exact replica calculations, and the island formula captures the leading semiclassical purification effect. In the large-entropy limit relevant to our models, higher-order gravitational corrections are suppressed by powers of G_N or 1/c, while the exponential dependence on scrambling time arises from the geometry itself and remains robust. We explicitly discuss that CFT interactions lie outside the present scope but are not expected to change the leading qualitative features. This provides the requested justification while acknowledging the approximation's limits. revision: partial

Circularity Check

0 steps flagged

No significant circularity; results from explicit CFT computations on dynamical backgrounds

full rationale

The paper's central claims follow from direct calculations of mutual information and entanglement in free-fermion CFT on time-dependent JT and RST evaporating geometries, using standard thermofield-double correlators and island purification. No equations reduce by construction to fitted inputs, self-definitions, or load-bearing self-citations; the parametric dialing of scrambling time and resulting suppression of spikes are outputs of the model dynamics rather than inputs. The derivation chain is self-contained against external CFT and gravity benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The work rests on standard 2d gravity and CFT assumptions plus the quasiparticle picture for entanglement memory; scrambling time is treated as a tunable parameter rather than derived.

free parameters (1)
  • black hole scrambling time
    Parametrically dialed in the models to interpolate between regimes; central to the suppression effect.
axioms (2)
  • domain assumption CFT admits quasiparticle description for entanglement dynamics
    Invoked to explain known late-time spikes in mutual information.
  • domain assumption Island-induced purification drives late-time revival
    Used to interpret the mechanism in the evaporating background.

pith-pipeline@v0.9.0 · 5508 in / 1319 out tokens · 50853 ms · 2026-05-07T10:38:19.946854+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

33 extracted references · 31 canonical work pages

  1. [1]

    Black holes as mirrors: Quantum information in random subsystems,

    P. Hayden and J. Preskill, “Black holes as mirrors: Quantum information in random subsystems,” JHEP09(2007), 120 [arXiv:0708.4025[hep-th]]

    work page arXiv 2007

  2. [2]

    Fast Scramblers

    Y. Sekino and L. Susskind, “Fast Scramblers,” JHEP10(2008), 065 [arXiv:0808.2096[hep-th]]

    work page Pith review arXiv 2008

  3. [3]

    Black holes and the butterfly effect

    S. H. Shenker and D. Stanford, “Black holes and the butterfly effect,” JHEP03 (2014), 067 [arXiv:1306.0622[hep-th]]

    work page Pith review arXiv 2014

  4. [4]

    Entanglement Scrambling in 2d Conformal Field Theory,

    C. T. Asplund, A. Bernamonti, F. Galli and T. Hartman, “Entanglement Scrambling in 2d Conformal Field Theory,” JHEP09(2015), 110arXiv:1506.03772[hep-th]

    work page arXiv 2015

  5. [5]

    Entanglement entropy and conformal field theory,

    P. Calabrese and J. Cardy, “Entanglement entropy and conformal field theory,” J. Phys. A42(2009), 504005arXiv:0905.4013[cond-mat.stat-mech]

    work page arXiv 2009

  6. [6]

    Mutual information after a local quench in conformal field theory,

    C. T. Asplund and A. Bernamonti, “Mutual information after a local quench in conformal field theory,” Phys. Rev. D89(2014) no.6, 066015arXiv:1311.4173 [hep-th]

    work page arXiv 2014

  7. [7]

    Entanglement Tsunami in (1+1)-Dimensions,

    S. Leichenauer and M. Moosa, “Entanglement Tsunami in (1+1)-Dimensions,” Phys. Rev. D92(2015), 126004arXiv:1505.04225[hep-th]

    work page arXiv 2015

  8. [8]

    Lower Dimensional Gravity,

    R. Jackiw, “Lower Dimensional Gravity,” Nucl. Phys. B252(1985), 343-356

    1985

  9. [9]

    Gravitation and Hamiltonian Structure in Two Space-Time Dimensions,

    C. Teitelboim, “Gravitation and Hamiltonian Structure in Two Space-Time Dimensions,” Phys. Lett. B126(1983), 41-45

    1983

  10. [10]

    The Endpoint of Hawking radiation,

    J. G. Russo, L. Susskind and L. Thorlacius, “The Endpoint of Hawking radiation,” Phys. Rev. D46(1992), 3444-3449 [arXiv:hep-th/9206070[hep-th]]

    work page arXiv 1992

  11. [11]

    Black hole thermodynamics and information loss in two-dimensions,

    T. M. Fiola, J. Preskill, A. Strominger and S. P. Trivedi, “Black hole thermodynamics and information loss in two-dimensions,” Phys. Rev. D50, 3987-4014 (1994)arXiv:hep-th/9403137[hep-th]

    work page arXiv 1994

  12. [12]

    Islands outside the horizon,

    A. Almheiri, R. Mahajan and J. Maldacena, “Islands outside the horizon,” arXiv:1910.11077[hep-th]

    work page arXiv 1910

  13. [13]

    Almheiri, T

    A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian and A. Tajdini, “Replica Wormholes and the Entropy of Hawking Radiation,” JHEP05(2020), 013 arXiv:1911.12333[hep-th]

    work page arXiv 2020

  14. [14]

    Replica wormholes and the black hole interior,

    G. Penington, S. H. Shenker, D. Stanford and Z. Yang, “Replica wormholes and the black hole interior,” JHEP03(2022), 205arXiv:1911.11977[hep-th]

    work page arXiv 2022

  15. [15]

    Islands in Asymptotically Flat 2D Gravity,

    T. Hartman, E. Shaghoulian and A. Strominger, “Islands in Asymptotically Flat 2D Gravity,” JHEP07(2020), 022arXiv:2004.13857[hep-th]

    work page arXiv 2020

  16. [16]

    Disrupting Entanglement of Black Holes,

    S. Leichenauer, “Disrupting Entanglement of Black Holes,” Phys. Rev. D90(2014) no.4, 046009 doi:10.1103/PhysRevD.90.046009arXiv:1405.7365[hep-th]

    work page doi:10.1103/physrevd.90.046009arxiv:1405.7365 2014

  17. [17]

    Bounding the Space of Holographic CFTs with Chaos

    E. Perlmutter, “Bounding the Space of Holographic CFTs with Chaos,” JHEP10 (2016), 069arXiv:1602.08272[hep-th]. – 27 –

    work page Pith review arXiv 2016

  18. [18]

    Ephemeral islands, plunging quantum extremal surfaces and BCFT channels,

    T. J. Hollowood, S. P. Kumar, A. Legramandi and N. Talwar, “Ephemeral islands, plunging quantum extremal surfaces and BCFT channels,” JHEP01(2022), 078 arXiv:2109.01895[hep-th]

    work page arXiv 2022

  19. [19]

    Solvable models of quantum black holes: a review on Jackiw–Teitelboim gravity,

    T. G. Mertens and G. J. Turiaci, “Solvable models of quantum black holes: a review on Jackiw–Teitelboim gravity,” Living Rev. Rel.26(2023) no.1, 4 arXiv:2210.10846[hep-th]

    work page arXiv 2023

  20. [20]

    Casini and M

    H. Casini and M. Huerta, “Entanglement entropy in free quantum field theory,” J. Phys. A42(2009), 504007arXiv:0905.2562[hep-th]

    work page arXiv 2009

  21. [21]

    Evanescent black holes,

    C. G. Callan, Jr., S. B. Giddings, J. A. Harvey and A. Strominger, “Evanescent black holes,” Phys. Rev. D45(1992) no.4, R1005arXiv:hep-th/9111056[hep-th]

    work page arXiv 1992

  22. [22]

    Semiclassical approach to black hole evaporation,

    D. A. Lowe, “Semiclassical approach to black hole evaporation,” Phys. Rev. D47 (1993), 2446-2453arXiv:hep-th/9209008[hep-th]

    work page arXiv 1993

  23. [23]

    Numerical analysis of black hole evaporation,

    T. Piran and A. Strominger, “Numerical analysis of black hole evaporation,” Phys. Rev. D48(1993), 4729-4734arXiv:hep-th/9304148[hep-th]

    work page arXiv 1993

  24. [24]

    Page Curve for an Evaporating Black Hole,

    F. F. Gautason, L. Schneiderbauer, W. Sybesma and L. Thorlacius, “Page Curve for an Evaporating Black Hole,” JHEP05(2020), 091arXiv:2004.00598[hep-th]

    work page arXiv 2020

  25. [25]

    Entanglement Dynamics in 2D CFT with Boundary: Entropic origin of JT gravity and Schwarzian QM,

    N. Callebaut and H. Verlinde, “Entanglement Dynamics in 2D CFT with Boundary: Entropic origin of JT gravity and Schwarzian QM,” JHEP05(2019), 045 arXiv:1808.05583[hep-th]

    work page arXiv 2019

  26. [26]

    Moving Mirrors, Page Curves, and Bulk Entropies in AdS2,

    I. A. Reyes, “Moving Mirrors, Page Curves, and Bulk Entropies in AdS2,” Phys. Rev. Lett.127, no.5, 051602 (2021)arXiv:2103.01230[hep-th]

    work page arXiv 2021

  27. [27]

    Boundary chaos,

    F. Fritzsch and T. Prosen, “Boundary chaos,” Phys. Rev. E106, no.1, 014210 (2022)arXiv:2112.05093[cond-mat.stat-mech]

    work page arXiv 2022

  28. [28]

    Boundary chaos: Exact entanglement dynamics,

    F. Fritzsch, R. Ghosh and T. Prosen, “Boundary chaos: Exact entanglement dynamics,” SciPost Phys.15, no.3, 092 (2023)arXiv:2301.08168 [cond-mat.stat-mech]

    work page arXiv 2023

  29. [29]

    Submerging islands through thermalization,

    V. Balasubramanian, B. Craps, M. Khramtsov and E. Shaghoulian, “Submerging islands through thermalization,” JHEP10, 048 (2021)arXiv:2107.14746[hep-th]

    work page arXiv 2021

  30. [30]

    A dynamical mechanism for the Page curve from quantum chaos,

    H. Liu and S. Vardhan, “A dynamical mechanism for the Page curve from quantum chaos,” JHEP03(2021), 088arXiv:2002.05734[hep-th]

    work page arXiv 2021

  31. [31]

    Spread of entanglement in a Sachdev-Ye-Kitaev chain,

    Y. Gu, A. Lucas and X. L. Qi, “Spread of entanglement in a Sachdev-Ye-Kitaev chain,” JHEP09(2017), 120arXiv:1708.00871[hep-th]

    work page arXiv 2017

  32. [32]

    Tunable Quantum Chaos in the Sachdev-Ye-Kitaev Model Coupled to a Thermal Bath,

    Y. Chen, H. Zhai and P. Zhang, “Tunable Quantum Chaos in the Sachdev-Ye-Kitaev Model Coupled to a Thermal Bath,” JHEP07(2017), 150 arXiv:1705.09818[hep-th]

    work page arXiv 2017

  33. [33]

    Replica wormhole and information retrieval in the SYK model coupled to Majorana chains,

    Y. Chen, X. L. Qi and P. Zhang, “Replica wormhole and information retrieval in the SYK model coupled to Majorana chains,” JHEP06(2020), 121arXiv:2003.13147 [hep-th]. – 28 –

    work page arXiv 2020