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Quantum adiabaticity in many-body systems and almost-orthogonality in complementary subspace
by Jyong-Hao Chen and Vadim Cheianov
Submission summary
| Authors (as registered SciPost users): | Jyong-Hao Chen |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202411_00033v2 (pdf) |
| Date accepted: | Oct. 21, 2025 |
| Date submitted: | Sept. 14, 2025, 10:43 a.m. |
| Submitted by: | Jyong-Hao Chen |
| Submitted to: | SciPost Physics Core |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
We investigate why, in quantum many-body systems, the adiabatic fidelity and the overlap between the initial state and instantaneous ground states often yield nearly identical values. Our analysis suggests that this phenomenon results from an interplay between two intrinsic limits of many-body systems: the limit of small evolution parameters and the limit of large system sizes. In the former case, conventional perturbation theory provides a straightforward explanation. In the latter case, a key insight is that pairs of vectors in the Hilbert space orthogonal to the initial state tend to become nearly orthogonal as the system size increases. We illustrate these general findings with two representative models of driven many-body systems: the driven Rice-Mele model and the driven interacting Kitaev chain model.
Author comments upon resubmission
We thank the referees for their careful reading and constructive comments on our manuscript.
We agree to transfer the manuscript to SciPost Physics Core.
In this revision, we have substantially improved the presentation in line with the referees’ requests.
Below we summarize the main changes.
For convenience, we provide a color-highlighted version of the manuscript showing all changes.
[link: https://www.dropbox.com/scl/fi/gbin3wzi0t0qrwf7yjksh/draft_adiabatic_closeness_20250913_color.pdf?rlkey=4qly8d38m9kj5p07ltvlory6d&st=0g0rj04t&dl=0]
A point-by-point response to each report will be submitted on the referee-report pages.
Sincerely,
Authors
List of changes
List of main changes
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Introduction (Sec. 1). We added a subsection, Summary of main results and contributions, that summarizes our main findings and contributions. We also added a paragraph clarifying the relation of our work to rigorous results on many-body adiabatic state preparation. The literature pointed out by Referee 1 is now cited as Refs. [24,46–51].
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Bound from Ref. [37]. As requested by Referee 2, the bound obtained in Ref. [37] now appears as Eq. (7).
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Figure 2 revised. We added a new fourth row that overlays the curves shown in the second and third rows, with a logarithmic vertical axis; the original fourth row is now the fifth. The caption and main text were updated accordingly.
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Finite-size scaling made explicit (Sec. 6). We added an unnumbered subsection titled Condition for adiabaticity breakdown revisited to make the finite-size scaling of the driving rate explicit.
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Summary and Outlook (Sec. 8). We slightly revised the second paragraph to address a confusion raised by Referee 2.
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Appendix A restored. We reinstated Appendix A: Alternative derivation of Eq. (17), which appears in our arXiv preprint but was omitted during journal submission. In- cluding this appendix improves self-containment and benefits readers, as the projection- operator technique—central to the present work and not used in Refs. [37,38]—is useful for extending the pure-state case treated here to mixed states.
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Other changes are minor.
Published as SciPost Phys. Core 8, 084 (2025)