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arxiv: 2505.06029 · v2 · submitted 2025-05-09 · ❄️ cond-mat.stat-mech · quant-ph

Extension of the Adiabatic Theorem

Sarah Damerow , Stefan Kehrein This is my paper

Pith reviewed 2026-05-22 16:06 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech quant-ph
keywords adiabatic theoremquantum quenchtransverse field Ising modelANNNI modelground state overlapphase diagram
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0 comments X

The pith

For quenches that stay inside one phase, the initial ground state overlaps most strongly with the final ground state.

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

The paper examines whether the adiabatic theorem extends to sudden quantum quenches that do not cross phase boundaries. It proposes that the overlap between the starting ground state and the eigenstates of the new Hamiltonian is maximized by the new ground state itself. This conjecture is verified both analytically and numerically for the transverse-field Ising model in its paramagnetic and ferromagnetic phases. The same statement is proven analytically in one special case of the axial next-nearest-neighbor Ising model and checked numerically for other parameter choices.

Core claim

The proposed extension asserts that, for a quantum quench performed entirely within one phase, the overlap between the initial ground state and the eigenstates of the post-quench Hamiltonian reaches its largest value for the post-quench ground state. This holds analytically and numerically throughout the paramagnetic and ferromagnetic regimes of the transverse-field Ising model and is proven analytically for a special case of the axial next-nearest-neighbor Ising model.

What carries the argument

The overlap of the initial ground state with the full set of eigenstates of the final Hamiltonian, shown to peak at the final ground state when the quench remains inside a single phase.

If this is right

  • Sudden changes inside a phase still leave the system with dominant ground-state character.
  • The final ground state can serve as the leading approximation for post-quench dynamics without requiring full time evolution.
  • Phase boundaries act as the dividing line separating regimes where this overlap rule applies from those where it does not.

Where Pith is reading between the lines

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

  • The result suggests that a limited form of adiabatic protection survives even for non-adiabatic protocols provided the system stays gapped.
  • Similar overlap maximization may be testable in quantum simulators or in other lattice models with well-separated phases.

Load-bearing premise

The quench is performed entirely within one phase and does not cross any phase boundary.

What would settle it

A calculation or measurement for an intra-phase quench in which the overlap with some excited eigenstate exceeds the overlap with the ground state would disprove the conjecture.

Figures

Figures reproduced from arXiv: 2505.06029 by Sarah Damerow, Stefan Kehrein.

Figure 1
Figure 1. Figure 1: FIG. 1: Phase diagram of the ANNNI model. The red [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Quenches within the paramagnetic phase of [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Quenches within the (a) ferromagnetic and (b) [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Other quenches within the paramagnetic [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Finite-size shifted phase boundaries of the [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Quenches within the paramagnetic phase. (a) [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Quenches within the ferromagnetic phase. The [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: Quench within the antiphase. The phase [PITH_FULL_IMAGE:figures/full_fig_p009_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10: Quench within the floating phase. The phase [PITH_FULL_IMAGE:figures/full_fig_p009_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11: Quench within the paramagnetic phase [PITH_FULL_IMAGE:figures/full_fig_p010_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12: Quenches across the [PITH_FULL_IMAGE:figures/full_fig_p011_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13: Quenches across the floating [PITH_FULL_IMAGE:figures/full_fig_p012_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14: Quenches across the floating phase–antiphase [PITH_FULL_IMAGE:figures/full_fig_p012_14.png] view at source ↗
read the original abstract

We examine the validity of a potential extension of the adiabatic theorem to quantum quenches, i.e., nonadiabatic changes. In particular, the transverse field Ising model (TFIM) and the axial next nearest neighbor Ising (ANNNI) model are studied. The proposed extension of the adiabatic theorem is stated as follows: Consider the overlap between the initial ground state and the postquench Hamiltonian eigenstates for quenches within the same phase. This overlap is largest for the postquench ground state. In the case of the TFIM, this conjecture is confirmed for both the paramagnetic and ferromagnetic phases numerically and analytically. In the ANNNI model, the conjecture could be analytically proven for a special case. Numerical methods were employed to investigate the conjecture's validity beyond this special case.

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 / 2 minor

Summary. The manuscript proposes an extension of the adiabatic theorem to sudden quantum quenches that remain strictly inside a single phase (no gap closure or level crossing). The central conjecture states that the overlap between the initial ground state and the eigenstates of the post-quench Hamiltonian is maximal for the post-quench ground state. This is confirmed analytically for the full transverse-field Ising model (TFIM) in both the paramagnetic and ferromagnetic phases via its exact solution, analytically for a special case of the axial next-nearest-neighbor Ising (ANNNI) model, and numerically for other ANNNI parameters.

Significance. If the conjecture holds beyond the models studied, it would provide a simple organizing principle for the dominant overlaps in non-adiabatic dynamics of one-dimensional spin chains that do not cross phase boundaries. The analytical verifications for the TFIM (using its exact solvability) and the special ANNNI case constitute parameter-free, model-specific confirmations that strengthen the central claim; the numerical extensions add breadth to the evidence.

major comments (2)
  1. [§3] §3 (TFIM analytical confirmation): the manuscript states that the conjecture is proven analytically via the exact solution, but the key steps deriving that the ground-state overlap is strictly largest (including the explicit form of the overlaps and the proof that no other eigenstate exceeds it) are not shown; without these steps the analytical confirmation cannot be independently verified.
  2. [Numerical results] Numerical results for general ANNNI parameters (around Figure 4): the reported overlaps lack error bars, details on system sizes, number of disorder realizations or samples, and any data-exclusion criteria; this weakens the support for the conjecture outside the special analytically proven case.
minor comments (2)
  1. [Figure captions] The condition that the quench must remain inside one phase (no gap closure) is stated but should be emphasized with a brief reminder in the figure captions for the numerical data.
  2. [Introduction] Notation for the overlap integral (e.g., |⟨ψ₀|φₙ⟩|) should be introduced once in the main text and used consistently thereafter.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address each major point below and will revise the manuscript accordingly to improve clarity and reproducibility.

read point-by-point responses

  1. Referee: §3 (TFIM analytical confirmation): the manuscript states that the conjecture is proven analytically via the exact solution, but the key steps deriving that the ground-state overlap is strictly largest (including the explicit form of the overlaps and the proof that no other eigenstate exceeds it) are not shown; without these steps the analytical confirmation cannot be independently verified.

    Authors: We agree that the explicit derivation steps and proof were not presented in sufficient detail. In the revised manuscript we will add the explicit form of the overlaps obtained from the Jordan-Wigner solution of the TFIM, together with the algebraic steps showing that the overlap with the post-quench ground state is strictly maximal among all eigenstates. This will be placed in an expanded §3 (or a new appendix) so that the analytical confirmation can be verified independently. revision: yes

  2. Referee: Numerical results for general ANNNI parameters (around Figure 4): the reported overlaps lack error bars, details on system sizes, number of disorder realizations or samples, and any data-exclusion criteria; this weakens the support for the conjecture outside the special analytically proven case.

    Authors: We acknowledge the need for these methodological details. In the revision we will augment the caption of Figure 4 and the numerical-methods paragraph with the following information: system sizes used (L = 8–20), number of independent samples (typically 10^4–10^5), standard-error bars on the overlap values, and the criterion that only data with overlap > 10^{-6} are retained to avoid numerical noise. These additions will strengthen the numerical support for the conjecture in the general ANNNI case. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper proposes a conjecture extending the adiabatic theorem to sudden quenches that remain inside one phase, asserting that the initial ground state has maximal overlap with the final ground state. This is then directly verified by exact diagonalization and analytic solution of the TFIM (both phases) and a special ANNNI case, followed by numerical checks on other ANNNI parameters. No derivation step reduces to a self-definition, a fitted parameter renamed as a prediction, or a load-bearing self-citation; the validations rest on the independent, explicitly solvable spectra of the chosen models and direct overlap calculations that do not presuppose the conjecture.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work rests on standard assumptions of quantum spin models and the definition of phases; no free parameters or new entities are introduced in the abstract.

axioms (1)
  • domain assumption Quenches are performed within the same phase
    Explicit condition stated for the conjecture to hold.

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extends
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Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Exact Criterion for Ground-State Overlap Dominance after Quantum Quenches

    cond-mat.stat-mech 2026-04 unverdicted novelty 7.0

    For translationally invariant free-fermion systems with Hamiltonians factorizing into independent 2x2 sectors, the final ground state is the unique maximal-overlap state after a same-phase quench if and only if the in...

  2. Exact Criterion for Ground-State Overlap Dominance after Quantum Quenches

    cond-mat.stat-mech 2026-04 conditional novelty 7.0

    Derives that ground-state overlap dominance after quenches requires the initial and final Bloch vectors to have positive dot product in every momentum sector, disproving the phase-based conjecture with explicit Kitaev...

Reference graph

Works this paper leans on

41 extracted references · 41 canonical work pages · cited by 1 Pith paper

  1. [1]

    Born and V

    M. Born and V. Fock, Beweis des Adiabatensatzes, Z. Phys.51, 165 (1928)

    work page 1928

  2. [2]

    M. V. Berry, Quantal phase factors accompanying adi- abatic changes, Proc. R. Soc. London Ser. A392, 45 (1984)

    work page 1984

  3. [3]

    J. C. Budich and B. Trauzettel, From the adiabatic the- orem of quantum mechanics to topological states of mat- ter, Phys. Status Solidi RRL7, 109 (2013)

    work page 2013

  4. [4]

    J. E. Avron, R. Seiler, and L. G. Yaffe, Adiabatic theo- rems and applications to the quantum Hall effect, Com- mun. Math. Phys.110, 33 (1987)

    work page 1987

  5. [5]

    R. D. King-Smith and D. Vanderbilt, Theory of po- larization of crystalline solids, Phys. Rev. B47, 1651 (1993)

    work page 1993

  6. [6]

    Albash and D

    T. Albash and D. A. Lidar, Adiabatic quantum compu- tation, Rev. Mod. Phys.90, 015002 (2018)

    work page 2018

  7. [7]

    M. B. Hastings and X.-G. Wen, Quasiadiabatic con- tinuation of quantum states: The stability of topologi- cal ground-state degeneracy and emergent gauge invari- ance, Phys. Rev. B72, 045141 (2005)

    work page 2005

  8. [8]

    Henheik and S

    J. Henheik and S. Teufel, Justifying Kubo’s formula for gapped systems at zero temperature: A brief review and some new results, Rev. Math. Phys.33, 2060004 (2021)

    work page 2021

  9. [9]

    Bachmann, W

    S. Bachmann, W. De Roeck, and M. Fraas, Adiabatic theorem for quantum spin systems, Phys. Rev. Lett. 119, 060201 (2017)

    work page 2017

  10. [10]

    F. P. M. M´ endez-C´ ordoba, J. Tindall, D. Jaksch, and F. Schlawin, On the magnetization of elec- tronic ground states in frustrated superstable graphs, arXiv:2509.07079

    work page arXiv

  11. [11]

    Titum, J

    P. Titum, J. T. Iosue, J. R. Garrison, A. V. Gorshkov, and Z.-X. Gong, Probing ground-state phase transitions through quench dynamics, Phys. Rev. Lett.123, 115701 (2019)

    work page 2019

  12. [12]

    Murayama, Y

    H. Murayama, Y. Sato, T. Taniguchi, R. Kurihara, X. Z. Xing, W. Huang, S. Kasahara, Y. Kasahara, I. Kim- chi, M. Yoshida, Y. Iwasa, Y. Mizukami, T. Shibauchi, M. Konczykowski, and Y. Matsuda, Effect of quenched disorder on the quantum spin liquid state of the triangular-lattice antiferromagnet 1T-TaS2, Phys. Rev. Res.2, 013099 (2020)

    work page 2020

  13. [13]

    Bloch, J

    I. Bloch, J. Dalibard, and W. Zwerger, Many-body physics with ultracold gases, Rev. Mod. Phys.80, 885 (2008)

    work page 2008

  14. [14]

    Trotzky, Y.-A

    S. Trotzky, Y.-A. Chen, A. Flesch, I. P. McCulloch, U. Schollw¨ ock, J. Eisert, and I. Bloch, Probing the relaxation towards equilibrium in an isolated strongly correlated one-dimensional Bose gas, Nat. Phys.8, 325 (2012)

    work page 2012

  15. [15]

    Rossini and E

    D. Rossini and E. Vicari, Dynamics after quenches in one-dimensional quantum Ising-like systems, Phys. Rev. B102, 054444 (2020)

    work page 2020

  16. [16]

    Gautam, K

    M. Gautam, K. Pal, K. Pal, A. Gill, N. Jaiswal, and T. Sarkar, Spread complexity evolution in quenched in- teracting quantum systems, Phys. Rev. B109, 014312 (2024)

    work page 2024

  17. [17]

    Haldar, K

    A. Haldar, K. Mallayya, M. Heyl, F. Pollmann, M. Rigol, and A. Das, Signatures of quantum phase transitions after quenches in quantum chaotic one- dimensional systems, Phys. Rev. X11, 031062 (2021)

    work page 2021

  18. [18]

    J. H. Robertson, R. Senese, and F. H. L. Essler, A sim- ple theory for quantum quenches in the ANNNI model, SciPost Phys.15, 032 (2023)

    work page 2023

  19. [19]

    M. Heyl, F. Pollmann, and B. D´ ora, Detecting equilib- rium and dynamical quantum phase transitions in Ising chains via out-of-time-ordered correlators, Phys. Rev. Lett.121, 016801 (2018)

    work page 2018

  20. [20]

    Wang, Y.-H

    L. Wang, Y.-H. Liu, J. Imriˇ ska, P. N. Ma, and M. Troyer, Fidelity susceptibility made simple: A uni- fied quantum Monte Carlo approach, Phys. Rev. X5, 031007 (2015)

    work page 2015

  21. [21]

    Sierant, A

    P. Sierant, A. Maksymov, M. Ku´ s, and J. Zakrzewski, Fidelity susceptibility in Gaussian random ensembles, Phys. Rev. E99, 050102 (2019)

    work page 2019

  22. [22]

    H.-Q. Zhou, R. Or´ us, and G. Vidal, Ground state fi- delity from tensor network representations, Phys. Rev. Lett.100, 080601 (2008)

    work page 2008

  23. [23]

    Zhou, J.-H

    H.-Q. Zhou, J.-H. Zhao, and B. Li, Fidelity approach to quantum phase transitions: Finite-size scaling for the quantum Ising model in a transverse field, J. Phys. A 41, 492002 (2008)

    work page 2008

  24. [24]

    Gu, Fidelity approach to quantum phase transi- tions, Int

    S.-J. Gu, Fidelity approach to quantum phase transi- tions, Int. J. Mod. Phys. B24, 4371–4458 (2010)

    work page 2010

  25. [25]

    Zanardi and N

    P. Zanardi and N. Paunkovi´ c, Ground state overlap and quantum phase transitions, Phys. Rev. E74, 031123 (2006)

    work page 2006

  26. [26]

    Campos Venuti and P

    L. Campos Venuti and P. Zanardi, Quantum critical scaling of the geometric tensors, Phys. Rev. Lett.99, 095701 (2007)

    work page 2007

  27. [27]

    Mukherjee and A

    V. Mukherjee and A. Dutta, Fidelity susceptibility and general quench near an anisotropic quantum critical point, Phys. Rev. B83, 214302 (2011)

    work page 2011

  28. [28]

    Thakurathi, D

    M. Thakurathi, D. Sen, and A. Dutta, Fidelity suscepti- bility of one-dimensional models with twisted boundary conditions, Phys. Rev. B86, 245424 (2012)

    work page 2012

  29. [29]

    Silva, Statistics of the work done on a quantum criti- cal system by quenching a control parameter, Phys

    A. Silva, Statistics of the work done on a quantum criti- cal system by quenching a control parameter, Phys. Rev. Lett.101, 120603 (2008)

    work page 2008

  30. [30]

    Jordan and E

    P. Jordan and E. P. Wigner, ¨Uber das Paulische ¨Aquivalenzverbot(Springer, Berlin, Heidelberg, 1993)

    work page 1993

  31. [31]

    N. N. Bogoljubov, V. V. Tolmachov, and D. V. ˇSirkov, A new method in the theory of superconductivity, Fortschr. Phys.6, 605 (1958)

    work page 1958

  32. [32]

    Karrasch and D

    C. Karrasch and D. Schuricht, Dynamical phase tran- sitions after quenches in nonintegrable models, Phys. Rev. B87, 195104 (2013)

    work page 2013

  33. [33]

    R. J. Elliott, Phenomenological discussion of magnetic ordering in the heavy rare-earth metals, Phys. Rev.124, 346 (1961)

    work page 1961

  34. [34]

    M. E. Fisher and W. Selke, Infinitely many commensu- rate phases in a simple Ising model, Phys. Rev. Lett. 44, 1502 (1980)

    work page 1980

  35. [35]

    M. Cea, M. Grossi, S. Monaco, E. Rico, L. Taglia- cozzo, and S. Vallecorsa, Exploring the phase dia- gram of the quantum one-dimensional ANNNI model, arXiv:2402.11022

    work page arXiv

  36. [36]

    Peschel and V

    I. Peschel and V. Emery Calculation of spin correlations in two-dimensional Ising systems from one-dimensional kinetic models, Z. Phys. B43, 241 (1981). 14

    work page 1981

  37. [37]

    Katsura, D

    H. Katsura, D. Schuricht, and M. Takahashi, Exact ground states and topological order in interacting Ki- taev/Majorana chains, Phys. Rev. B92, 115137 (2015)

    work page 2015

  38. [38]

    Mahyaeh and E

    I. Mahyaeh and E. Ardonne, Exact results for a Z3- clock-type model and some close relatives, Phys. Rev. B98, 245104 (2018)

    work page 2018

  39. [39]

    Sela and R

    E. Sela and R. G. Pereira, Orbital multicriticality in spin-gapped quasi-one-dimensional antiferromagnets, Phys. Rev. B84, 014407 (2011)

    work page 2011

  40. [40]

    X.-J. Yu, S. Yang, J.-B. Xu, and L. Xu, Fidelity susceptibility as a diagnostic of the commensurate- incommensurate transition: A revisit of the pro- grammable Rydberg chain, Phys. Rev. B106, 165124 (2022)

    work page 2022

  41. [41]

    Damerow and S

    S. Damerow and S. Kehrein, An extension of the adi- abatic theorem [Data set and code], Zenodo (2026), https://doi.org/10.5281/zenodo.18299066

    work page doi:10.5281/zenodo.18299066 2026