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arxiv: 2605.05106 · v1 · submitted 2026-05-06 · ❄️ cond-mat.stat-mech · quant-ph

Kink-kink correlations in nonlinear quenches across a quantum critical point

Lakshita Jindal , Kavita Jain This is my paper

Pith reviewed 2026-05-08 16:08 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech quant-ph
keywords kink-kink correlationsnonlinear quenchesKibble-Zurek mechanismtransverse field Ising modeldephasing lengthcompressed exponentialadiabatic perturbation theory
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The pith

For algebraic quenches in the transverse-field Ising model, kink-kink correlations depend only on the Kibble-Zurek length when the quench is superlinear; otherwise they require an additional dephasing length and decay as a compressed-expon-

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

The paper examines how nonlinear quenches across a quantum critical point affect higher-order correlation functions in the one-dimensional transverse-field Ising model. It shows that the equal-time longitudinal kink-kink correlator at the end of the quench is not always captured by the Kibble-Zurek length alone. For superlinear algebraic quenches the correlator is a universal function of distance in units of the KZ length. For slower quenches an extra length scale arising from phase differences between modes is needed, and the resulting dephased correlator follows a compressed-exponential form whose power changes continuously with the quench exponent. This extends the KZ paradigm beyond defect densities to two-point functions and reveals new scaling structures controlled by quench nonlinearity.

Core claim

Using adiabatic perturbation theory, analytical arguments and numerical integration, the authors establish that the kink-kink correlation function after an algebraic quench depends only on the KZ length for superlinear protocols. For linear and sublinear protocols an additional dephasing length is required. The dephased correlator decays as exp[−(r/ξ)^α] where the exponent α varies continuously with the quench exponent.

What carries the argument

Adiabatic perturbation theory applied to the Bogoliubov-de Gennes equations of the TFIM, which yields the mode occupation numbers and the relative phases between low-energy modes that determine the kink-kink correlator.

If this is right

  • The kink-kink correlator becomes a universal function of the scaled distance for all superlinear algebraic quenches.
  • An extra dephasing length appears and controls the correlator when the quench exponent is less than or equal to one.
  • The decay of the dephased correlator is a compressed exponential whose stretching exponent interpolates continuously between different values as the quench exponent is varied.
  • The KZ mechanism must be supplemented by phase information to capture two-point functions in general nonlinear quenches.

Where Pith is reading between the lines

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

  • Analogous dephasing scales and compressed-exponential forms may appear in other integrable critical systems with linear dispersion.
  • Ultracold-atom or ion-trap experiments could measure the continuous change of the decay exponent by varying the quench protocol.
  • The results suggest that coherence between distant modes survives the quench and shapes spatial correlations beyond simple defect counting.

Load-bearing premise

Adiabatic perturbation theory accurately captures the non-adiabatic transitions and the phases of the low-lying modes produced by the algebraic quench across the critical point.

What would settle it

A numerical computation of the exact time evolution for the TFIM under an algebraic quench that reveals either dependence on a length scale other than KZ and dephasing, or a decay form that is not compressed exponential with quench-dependent exponent.

Figures

Figures reproduced from arXiv: 2605.05106 by Kavita Jain, Lakshita Jindal.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) The nonlinear quench protocol ( view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) Energy level diagram obtained on using Eq. ( view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Excitation probability, view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (a) Dephased correlator, view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Scaled off-diagonal kink-kink correlator as a function of scaled distance for (a) view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. (a) Peak height and the peak position in view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. (a) Magnitude of the dephased correlator at the end of the quench in the limit view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Off-diagonal correlator for view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Longitudinal mean defect density as a function of view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Off-diagonal correlator at the end of quench as a function of distance for view at source ↗
read the original abstract

When a quantum system exhibiting a second order phase transition is quenched across the critical point in large but finite time, the dynamics are not adiabatic in the critical region and the Kibble-Zurek (KZ) mechanism provides a framework to determine local observables such as the mean defect density. However, to find higher-point functions, one has to go beyond the KZ paradigm asshown in recent works on one-dimensional transverse field Ising model (TFIM) following a linear quench. It has been found that (i) besides the KZ scale, the quench dynamics depend on another length scale that arises due to the finite phase difference between the low energy modes, and (ii) contrary to the expectations based on the KZ mechanism, in general, the correlation functions do not decay exponentially with distance. Motivated by these results for the linear quench, we are interested in understanding if these properties are universal, and consider the 1D TFIM when the transverse field varies algebraically in the vicinity of the critical field. We focus on the equal-time,longitudinal kink-kink correlation function at the end of the quench from the paramagnetic to the ferromagnetic phase, and find that (i) the correlator depends only on the KZ length for superlinear quenches, otherwise an additional dephasing length is required to describe it, and (ii) the dephased correlator decays as a compressed exponential with an exponent that changes continuously with the quench exponent. Our results are obtained using an adiabatic perturbation theory, analytical arguments and exact numerical integration of the relevant equations.

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

0 major / 2 minor

Summary. The manuscript studies the equal-time longitudinal kink-kink correlation function in the 1D transverse-field Ising model after algebraic (nonlinear) quenches of the transverse field across the quantum critical point from paramagnetic to ferromagnetic phase. Employing adiabatic perturbation theory to obtain mode occupations and phases, together with scaling arguments and direct numerical integration of the time-dependent Bogoliubov-de Gennes equations, the authors conclude that the correlator depends only on the Kibble-Zurek length for superlinear quenches; for sublinear quenches an additional dephasing length is required, and the dephased correlator decays as a compressed exponential whose exponent varies continuously with the quench exponent.

Significance. If the central claims hold, the work usefully generalizes prior linear-quench results to the algebraic case, demonstrating that the necessity of a dephasing scale and the compressed-exponential form are robust features of the post-quench correlations. The combination of analytic perturbation theory with exact numerical solution of the mode equations supplies an internal consistency check that is stronger than typical KZ studies relying solely on scaling or mean-field approximations.

minor comments (2)
  1. The abstract contains the typographical error 'asshown' (should be 'as shown').
  2. Section 3 (or wherever the dephasing length is introduced) would benefit from an explicit equation defining the dephasing length in terms of the mode phases before it is used in the scaling arguments.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of our manuscript and the recommendation to accept. The referee's summary correctly captures our central results on the longitudinal kink-kink correlator after algebraic quenches in the 1D TFIM, including the distinction between superlinear and sublinear cases and the form of the dephased decay.

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained via standard TFIM methods

full rationale

The paper's central results on kink-kink correlations for algebraic quenches follow from adiabatic perturbation theory applied to the TFIM mode equations, supplemented by scaling arguments and direct numerical solution of the time-dependent Bogoliubov-de Gennes equations. These steps are independent of the claimed functional forms and scaling behaviors; the numerics provide an external consistency check rather than a fit or redefinition. The reference to prior linear-quench results is motivational and not load-bearing for the nonlinear case. No self-definitional reductions, fitted inputs renamed as predictions, or uniqueness theorems imported from self-citations appear in the derivation chain.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Relies on exact solvability of 1D TFIM via Jordan-Wigner and applicability of adiabatic perturbation theory; no new free parameters or entities introduced.

axioms (2)
  • standard math The 1D TFIM is exactly solvable by Jordan-Wigner transformation allowing numerical integration of time-dependent modes
    Enables exact numerical results for the correlator
  • domain assumption Adiabatic perturbation theory captures leading non-adiabatic corrections near the critical point
    Used to derive analytical dependence on KZ and dephasing lengths

pith-pipeline@v0.9.0 · 9931 in / 1227 out tokens · 65698 ms · 2026-05-08T16:08:31.112916+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

73 extracted references · 73 canonical work pages

  1. [1]

    and emerging quantum technologies [ 2–4]. As an example, consider adiabatic quantum computing [ 3] in which starting from an easy-to-prepare ground state of a quantum system, the Hamiltonian is varied slowly so as to arrive at the ground state of a Hamiltonian that encodes the solution of a complex problem. However, if a phase transition occurs during suc...

    work page 2000

  2. [2]

    Similarly, the second term in Eq

    = eiΘ1cτ ω + 1 cτ ω (ω + 1)2 sin( π 2ω )F ω (B.9) Assuming that the contour can be deformed such that it passes through the saddle points where the integral C1 does not diverge with R, the function h1 is evaluated at those saddle points where cos Θ1 < 0. Similarly, the second term in Eq. ( B.1) gives b2 = 2 sin( π 2ω )G which yields h2(x∗

    work page

  3. [3]

    ( B.1), b3 = −ie iπ 2ω (F + G) so that the saddles occur at x∗ 3 ∝ ei(2m+1)π(ω+1)e− iπ(ω+1) 2ω and Eq

    = eiΘ1cτ ω + 1 cτ ω (ω + 1)2 sin( π 2ω )G ω (B.10) For the third term in Eq. ( B.1), b3 = −ie iπ 2ω (F + G) so that the saddles occur at x∗ 3 ∝ ei(2m+1)π(ω+1)e− iπ(ω+1) 2ω and Eq. ( B.7) then gives h3(x∗

    work page

  4. [4]

    Finally, for the fourth term in Eq

    = eiΘ3cτ ω + 1 cτ ω (ω + 1)(F + G) ω (B.11) where Θ3 = (2m + 1)πω with non-negative integer m chosen such that cos Θ3 < 0. Finally, for the fourth term in Eq. ( B.1), b4 = ie− iπ 2ω (F + G), the saddles occur at x∗ 4 ∝ e iπ(ω+1) 2ω , and Eq. ( B.7) yields h4(x∗

    work page

  5. [5]

    ( B.1) by its modulus, and the rest of the discussion above remains unchanged

    = − cτ ω + 1 cτ ω (ω + 1)(F + G) ω (B.12) When sin( π 2ω ) < 0, the excitation probability is obtained on replacing sin ( π 2ω ) in Eq. ( B.1) by its modulus, and the rest of the discussion above remains unchanged. For sin ( π 2ω ) = 0 , pk ≈ π2 36 [2 + eiX(−1)n(F +G) + h.c.] for ω = (2 n)−1, n = 1 , 2, 3.... The first term in pk gives R π 0 dk 2 cos(kr) ...

    work page 2000

  6. [6]

    Sachdev, Cambridge University Press (2011)

    S. Sachdev, Cambridge University Press (2011)

    work page 2011

  7. [7]

    I. M. Georgescu, S. Ashhab, and F. Nori, Rev. Mod. Phys. 86, 153 (2014)

    work page 2014

  8. [8]

    Albash and D

    T. Albash and D. A. Lidar, Rev. Mod. Phys. 90, 015002 (2018)

    work page 2018

  9. [9]

    M. O. Scully and W. G. Unruh, Science 390, 998 (2025)

    work page 2025

  10. [10]

    T. W. B. Kibble, J. Phys. A 9, 1387 (1976)

    work page 1976

  11. [11]

    W. H. Zurek, Nature 317, 505 (1985)

    work page 1985

  12. [12]

    Damski, Physical review letters 95, 035701 (2005)

    B. Damski, Physical review letters 95, 035701 (2005)

    work page 2005

  13. [13]

    Damski and W

    B. Damski and W. H. Zurek, Physical Review A—Atomic, Molecular, and Optical Physics 73, 063405 (2006)

    work page 2006

  14. [14]

    Sadhukhan, A

    D. Sadhukhan, A. Sinha, A. Francuz, J. Stefaniak, M. M. Rams, J. Dziarmaga, and W. H. Zurek, Phys. Rev. B 101, 144429 (2020)

    work page 2020

  15. [15]

    Suzuki and W

    F. Suzuki and W. H. Zurek, Proceedings of the National Academy of Sciences 122, e2523903122 (2025)

    work page 2025

  16. [16]

    Jelić and L

    A. Jelić and L. Cugliandolo, J. Stat. Mech. , P02032 (2011)

    work page 2011

  17. [17]

    Jain, EPL 116, 26003 (2016)

    Priyanka and K. Jain, EPL 116, 26003 (2016)

    work page 2016

  18. [18]

    Ricateau, L

    H. Ricateau, L. F. Cugliandolo, and M. Picco, J. Stat. Mech. , P013201 (2018)

    work page 2018

  19. [19]

    Jeong, B

    K. Jeong, B. Kim, and S. J. Lee, Phys. Rev. E 102, 012114 (2020)

    work page 2020

  20. [20]

    Su and A

    Z. Su and A. J. Millis, Phys. Rev. X 10, 021028 (2020)

    work page 2020

  21. [21]

    Chatterjee, and K

    Priyanka, S. Chatterjee, and K. Jain, Journal of Statistical Mechanics: Theory and Experi- ment 2021, 033208 (2021)

    work page 2021

  22. [22]

    Jeong, B

    K. Jeong, B. Kim, and S. J. Lee, Journal of the Korean Physical Society 81, 811 (2022)

    work page 2022

  23. [23]

    Jindal and K

    L. Jindal and K. Jain, Physical Review E 109, 054116 (2024)

    work page 2024

  24. [24]

    C. Tang, K. Sfairopoulos, W. Zhang, and C. Ding, Physical Review E 112, 024111 (2025)

    work page 2025

  25. [25]

    Shu, L.-Y

    Y.-R. Shu, L.-Y. Yang, and S. Yin, Physical Review B 113, 134303 (2026)

    work page 2026

  26. [26]

    D. Sen, K. Sengupta, and S. Mondal, Physical Review Letters 101, 016806 (2008)

    work page 2008

  27. [27]

    Kolodrubetz, B

    M. Kolodrubetz, B. K. Clark, and D. A. Huse, Phys. Rev. Lett. 109, 015701 (2012)

    work page 2012

  28. [28]

    Puskarov and D

    T. Puskarov and D. Schuricht, SciPost Phys. 1, 003 (2016)

    work page 2016

  29. [29]

    del Campo, Phys

    A. del Campo, Phys. Rev. Lett. 121, 200601 (2018) . 29

    work page 2018

  30. [30]

    Zamora, G

    A. Zamora, G. Dagvadorj, P. Comaron, I. Carusotto, N. P. Proukakis, and M. H. Szymańska, Phys. Rev. Lett. 125, 095301 (2020)

    work page 2020

  31. [31]

    Schmitt, M

    M. Schmitt, M. M. Rams, J. Dziarmaga, M. Heyl, and W. H. Zurek, Science Advances 8, eabl6850 (2022)

    work page 2022

  32. [32]

    Kou and P

    H.-C. Kou and P. Li, Physical Review B 108, 214307 (2023)

    work page 2023

  33. [33]

    Suzuki and W

    F. Suzuki and W. H. Zurek, Physical review letters 132, 241601 (2024)

    work page 2024

  34. [34]

    Jindal and K

    L. Jindal and K. Jain, Phys. Rev. B 112, 014419 (2025)

    work page 2025

  35. [35]

    Soto-Garcia and N

    J. Soto-Garcia and N. Chepiga, Physical Review B 113, 085430 (2026)

    work page 2026

  36. [36]

    Maegochi, K

    S. Maegochi, K. Ienaga, and S. Okuma, Physical Review Letters 129, 227001 (2022)

    work page 2022

  37. [37]

    K. Du, X. Fang, C. Won, C. De, F.-T. Huang, W. Xu, H. You, F. J. Gómez-Ruiz, A. del Campo, and S.-W. Cheong, Nature Physics , 1 (2023)

    work page 2023

  38. [38]

    H. Wang, X. Li, and C. Li, Nature Communications 16, 10584 (2025)

    work page 2025

  39. [39]

    B. Ko, J. W. Park, and Y.-i. Shin, Nature physics 15, 1227 (2019)

    work page 2019

  40. [40]

    K. Lee, S. Kim, T. Kim, and Y.-i. Shin, Nature Physics 20, 1570 (2024)

    work page 2024

  41. [41]

    Labeyrie and R

    G. Labeyrie and R. Kaiser, Physical Review Letters 117, 275701 (2016)

    work page 2016

  42. [42]

    Cheng, Y.-K

    Z.-J. Cheng, Y.-K. Wu, S.-J. Li, and et al., Science Advances 10, eadr9527 (2024) , https://science.org

    work page 2024

  43. [43]

    Deutschländer, P

    S. Deutschländer, P. Dillmann, G. Maret, and P. Keim, Proc. Natl. Acad. Sci. 112, 20 , 6925 (2015)

    work page 2015

  44. [44]

    Libál, A

    A. Libál, A. del Campo, C. Nisoli, C. Reichhardt, and C. J. O. Reichhardt, Phys. Rev. Res. 2, 033433 (2020)

    work page 2020

  45. [45]

    L. Wang, C. Zhou, T. Tu, H.-W. Jiang, G.-P. Guo, and G.-C. Guo, Phys. Rev. A 89, 022337 (2014)

    work page 2014

  46. [46]

    Bando, Y

    Y. Bando, Y. Susa, H. Oshiyama, N. Shibata, M. Ohzeki, F. J. Gómez-Ruiz, D. A. Lidar, S. Suzuki, A. Del Campo, and H. Nishimori, Physical Review Research 2, 033369 (2020)

    work page 2020

  47. [47]

    A. D. King, S. Suzuki, J. Raymond, and et al., Nature Physics 18, 1324 (2022)

    work page 2022

  48. [48]

    Miessen, D

    A. Miessen, D. J. Egger, I. Tavernelli, and G. Mazzola, PRX Quantum 5, 040320 (2024)

    work page 2024

  49. [49]

    Dziarmaga, Adv

    J. Dziarmaga, Adv. Phys. 59, 1063 (2010)

    work page 2010

  50. [50]

    Polkovnikov, K

    A. Polkovnikov, K. Sengupta, A. Silva, and M. Vengalattore, Rev. Mod. Phys. 83, 863 (2011)

    work page 2011

  51. [51]

    Dutta, G

    A. Dutta, G. Aeppli, B. K. Chakrabarti, U. Divakaran, T. F. Rosenbaum, and D. Sen, Cam- bridge University Press, Delhi (2015). 30

    work page 2015

  52. [52]

    del Campo and W

    A. del Campo and W. H. Zurek, Int. J. Mod. Phys. A 29, 1430018 (2014)

    work page 2014

  53. [53]

    Dziarmaga, Phys

    J. Dziarmaga, Phys. Rev. Lett., 95(24) 245701 (2005)

    work page 2005

  54. [54]

    Garanin and R

    D. Garanin and R. Schilling, Physical Review B 66, 174438 (2002)

    work page 2002

  55. [55]

    Barankov and A

    R. Barankov and A. Polkovnikov, Physical review letters 101, 076801 (2008)

    work page 2008

  56. [56]

    R. W. Cherng and L. S. Levitov, Phys. Rev. A 73, 043614 (2006)

    work page 2006

  57. [57]

    Cincio, J

    L. Cincio, J. Dziarmaga, M. M. Rams, and W. H. Zurek, Phys. Rev. A 75, 052321 (2007)

    work page 2007

  58. [58]

    Roychowdhury, R

    K. Roychowdhury, R. Moessner, and A. Das, Physical Review B 104, 014406 (2021)

    work page 2021

  59. [59]

    R. J. Nowak and J. Dziarmaga, Physical Review B 104, 075448 (2021)

    work page 2021

  60. [60]

    Dziarmaga and M

    J. Dziarmaga and M. M. Rams, Physical Review B 106, 014309 (2022)

    work page 2022

  61. [61]

    Polkovnikov, Phys

    A. Polkovnikov, Phys. Rev. B 72, 161201(R) (2005)

    work page 2005

  62. [62]

    De Grandi and A

    C. De Grandi and A. Polkovnikov, Quantum Quenching, Annealing and Computation , 75 (2010)

    work page 2010

  63. [63]

    Ashhab, O

    S. Ashhab, O. A. Ilinskaya, and S. N. Shevchenko, Physical Review A 106, 062613 (2022)

    work page 2022

  64. [64]

    G. B. Mbeng, A. Russomanno, and G. E. Santoro, SciPost Physics Lecture Notes , 082 (2024)

    work page 2024

  65. [65]

    Barouch, B

    E. Barouch, B. M. McCoy, and M. Dresden, Physical Review A 2, 1075 (1970)

    work page 1970

  66. [66]

    Calabrese, F

    P. Calabrese, F. H. L. Essler, and M. Fagotti, Physical Review Letters 106, 227203 (2011)

    work page 2011

  67. [67]

    Calabrese, F

    P. Calabrese, F. H. L. Essler, and M. Fagotti, Journal of Statistical Mechanics: Theory and Experiment 2012, P07016 (2012)

    work page 2012

  68. [68]

    O. V. Ivakhnenko, S. N. Shevchenko, and F. Nori, Physics Reports 995, 1 (2023)

    work page 2023

  69. [69]

    C. M. Bender and S. A. Orszag, McGraw-Hill Book Company,New York, NY (1978)

    work page 1978

  70. [70]

    Rigol, V

    M. Rigol, V. Dunjko, V. Yurovsky, and M. Olshanii, Phys. Rev. Lett. 98, 050405 (2007)

    work page 2007

  71. [71]

    Vidmar and M

    L. Vidmar and M. Rigol, Journal of Statistical Mechanics: Theory and Experiment 2016, 064007 (2016)

    work page 2016

  72. [72]

    M. Heyl, A. Polkovnikov, and S. Kehrein, Phys. Rev. Lett. 110, 135704 (2013)

    work page 2013

  73. [73]

    Heyl, Reports on Progress in Physics 81, 054001 (2018)

    M. Heyl, Reports on Progress in Physics 81, 054001 (2018) . 31

    work page 2018