Comment on "Extension of the adiabatic theorem"

Jie Gu

arxiv: 2604.16439 · v2 · submitted 2026-04-07 · ❄️ cond-mat.stat-mech · quant-ph

Comment on "Extension of the adiabatic theorem"

Jie Gu This is my paper

Pith reviewed 2026-05-10 19:41 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech quant-ph

keywords quantum quenchadiabatic theoremfree fermionscounterexamplemany-body systemsgapped Hamiltoniansoverlap

0 comments

The pith

The conjecture that post-quench ground-state overlaps are always maximal within the same phase is disproved by a free-fermion counterexample.

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

This paper challenges a recent conjecture about quantum quenches in gapped systems. The conjecture claimed that when two Hamiltonians are in the same phase and connected by a gapped path, the initial ground state has the largest overlap with the post-quench ground state compared to other eigenstates. The authors construct an explicit local and translationally invariant free-fermion model that satisfies all the stated conditions yet violates the maximal overlap property. A sympathetic reader would care because this affects how we understand the robustness of the adiabatic theorem and the behavior of many-body systems after sudden changes.

Core claim

We show that the conjecture is not valid in general. An explicit local, translationally invariant, gapped free-fermion counterexample exists even though the pre- and postquench Hamiltonians are connected by a symmetry-preserving gapped path and the thermodynamic-limit spectrum is continuous.

What carries the argument

An explicit local, translationally invariant, gapped free-fermion Hamiltonian that serves as a counterexample to the conjecture while satisfying all its conditions.

If this is right

The maximal overlap need not occur with the postquench ground state even for quenches within the same phase.
Extensions of the adiabatic theorem based on this conjecture require modification.
The continuity of the spectrum in the thermodynamic limit and the existence of a gapped path do not guarantee the conjectured overlap behavior.
The property fails in free-fermion systems, suggesting it may not hold more broadly.

Where Pith is reading between the lines

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

This indicates that additional conditions beyond gapped paths may be necessary for the overlap property to hold.
Similar counterexamples could be sought in interacting systems to test the generality of the failure.
The result highlights potential subtleties in how symmetries and gaps constrain quench dynamics in lattice models.

Load-bearing premise

The assumption that satisfying the conditions of same phase, gapped connecting path, local translation invariance, and continuous spectrum is sufficient for the maximal ground-state overlap to hold.

What would settle it

Explicit calculation of the overlaps between the initial ground state and the post-quench eigenstates in the constructed free-fermion model; observation that the ground-state overlap is not the largest would confirm the disproof.

read the original abstract

Phys. Rev. B 113, 165102 (2026) proposed the conjecture that, for quantum quenches within the same phase, the overlap between the initial ground state and postquench eigenstates is maximal for the postquench ground state. We show that this conjecture is not valid in general. An explicit local, translationally invariant, gapped free-fermion counterexample exists even though the pre- and postquench Hamiltonians are connected by a symmetry-preserving gapped path and the thermodynamic-limit spectrum is continuous.

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.

Desk Editor's Note private letter to a colleague

This comment gives an explicit free-fermion counterexample that violates the overlap conjecture, provided the interpolation path stays gapped everywhere.

read the letter

This comment paper supplies an explicit local, translationally invariant free-fermion model that violates the conjecture from the 2026 Phys. Rev. B paper. The pre- and post-quench Hamiltonians sit in the same phase, connect through a symmetry-preserving path, and keep a continuous spectrum in the thermodynamic limit, yet the initial ground state does not have maximal overlap with the post-quench ground state. That is the central new point: a concrete counterexample rather than a general argument against the claim. Free-fermion models allow exact diagonalization, so the overlaps and single-particle spectrum can be computed directly, which is a clear strength here. The construction is also local and translationally invariant, matching the conditions the original conjecture appears to require. The soft spot is the gapped-path condition. The conjecture demands that the Hamiltonians remain gapped for every value of the interpolation parameter. In a free-fermion system this means the single-particle bands stay strictly positive for all momenta and all lambda in [0,1]. If the gap closes or touches zero at any intermediate point, the counterexample does not apply. The abstract asserts the path is gapped, but the Hamiltonian details and gap plots need checking to confirm no hidden closing occurs. Minor points include verifying that the symmetry is preserved throughout and that the thermodynamic-limit continuity holds as stated. This is useful for people working on adiabatic theorems, quantum quenches, and many-body dynamics in condensed matter and quantum information. Anyone who has cited or plans to use the original conjecture should see the counterexample. It deserves peer review as a comment because a verified disproof would correct how overlaps are modeled in these settings. Referees should focus on the gap along the full path and the overlap calculations.

Referee Report

1 major / 0 minor

Summary. The manuscript claims to disprove the conjecture from Phys. Rev. B 113, 165102 (2026) that, for quantum quenches within the same phase, the overlap between the initial ground state and postquench eigenstates is maximal for the postquench ground state. It constructs an explicit local, translationally invariant, gapped free-fermion model in which the pre- and post-quench Hamiltonians lie in the same phase, are connected by a symmetry-preserving gapped path, and exhibit a continuous thermodynamic-limit spectrum, yet the overlap is not maximal for the postquench ground state.

Significance. If the counterexample is valid, the result would be significant because it supplies a concrete, exactly solvable disproof of the conjecture using a free-fermion system that permits direct computation of overlaps and spectra. This would demonstrate that the proposed extension of the adiabatic theorem does not hold under the stated conditions even when all listed requirements (same phase, gapped path, continuous spectrum) are satisfied. The choice of a translationally invariant free-fermion model is a strength, as it allows analytic verification rather than numerical fitting.

major comments (1)

[Hamiltonian construction and interpolation path] The validity of the counterexample hinges on the interpolation path remaining gapped for every λ ∈ [0,1]. The manuscript must explicitly demonstrate that the minimum single-particle gap stays strictly positive across the entire path (for all momenta k and all λ), for example by providing the dispersion relation or a plot of gap(λ). Without this verification, it cannot be confirmed that the construction satisfies the conjecture's gapped-path condition, which is load-bearing for the disproof.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for identifying the need for explicit verification of the gapped interpolation path. We address the comment below and will revise the manuscript accordingly.

read point-by-point responses

Referee: [Hamiltonian construction and interpolation path] The validity of the counterexample hinges on the interpolation path remaining gapped for every λ ∈ [0,1]. The manuscript must explicitly demonstrate that the minimum single-particle gap stays strictly positive across the entire path (for all momenta k and all λ), for example by providing the dispersion relation or a plot of gap(λ). Without this verification, it cannot be confirmed that the construction satisfies the conjecture's gapped-path condition, which is load-bearing for the disproof.

Authors: We agree that an explicit demonstration is required to confirm the path remains gapped. The manuscript asserts that the pre- and post-quench Hamiltonians are connected by a symmetry-preserving gapped path but does not include the requested verification of the minimum gap. In the revised version we will add the single-particle dispersion relation of the interpolated Hamiltonian and either an analytic proof or a plot demonstrating that the gap remains strictly positive for all λ ∈ [0,1] and all momenta k. Because the model is free-fermion and translationally invariant, the gap is obtained directly from the eigenvalues of the momentum-space matrix, permitting an exact calculation. revision: yes

Circularity Check

0 steps flagged

Independent counterexample construction; no circularity

full rationale

The paper's central claim is established by explicit construction of a local, translationally invariant free-fermion Hamiltonian that satisfies every listed condition of the original conjecture (same phase, symmetry-preserving gapped interpolation path, continuous thermodynamic-limit spectrum) while violating the overlap maximality statement. This is an external model built from standard tight-binding terms, not a redefinition of conjecture quantities, a fitted parameter renamed as prediction, or a load-bearing self-citation. No equations reduce to their inputs by construction, and the argument remains self-contained against the stated assumptions.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The claim rests on the existence of one concrete free-fermion Hamiltonian that obeys the conjecture's stated conditions while violating its conclusion; no additional free parameters or invented entities are introduced.

axioms (1)

domain assumption The pre- and post-quench Hamiltonians are local, translationally invariant, gapped free-fermion operators connected by a symmetry-preserving gapped path with continuous thermodynamic-limit spectrum.
This is the minimal set of conditions the counterexample must satisfy to invalidate the conjecture.

pith-pipeline@v0.9.0 · 5369 in / 1208 out tokens · 44459 ms · 2026-05-10T19:41:26.195336+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

2 extracted references · 2 canonical work pages · 1 internal anchor

[1]

Damerow and S

S. Damerow and S. Kehrein, Phys. Rev. B113, 165102 (2026)

work page 2026
[2]

Exact Criterion for Ground-State Overlap Dominance after Quantum Quenches

T. Haque, Exact Criterion for Ground-State Overlap Dominance after Quantum Quenches, arXiv:2604.11420

work page internal anchor Pith review Pith/arXiv arXiv

[1] [1]

Damerow and S

S. Damerow and S. Kehrein, Phys. Rev. B113, 165102 (2026)

work page 2026

[2] [2]

Exact Criterion for Ground-State Overlap Dominance after Quantum Quenches

T. Haque, Exact Criterion for Ground-State Overlap Dominance after Quantum Quenches, arXiv:2604.11420

work page internal anchor Pith review Pith/arXiv arXiv