arxiv: 2602.01943 · v2 · submitted 2026-02-02 · 🪐 quant-ph · cond-mat.mes-hall· cond-mat.quant-gas· cond-mat.stat-mech· math-ph· math.MP

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Universal scaling of finite-temperature quantum adiabaticity in driven many-body systems

Li-Ying Chou , Jyong-Hao Chen

Authors on Pith no claims yet

Pith reviewed 2026-05-16 08:27 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.mes-hallcond-mat.quant-gascond-mat.stat-mechmath-phmath.MP

keywords finite-temperature adiabaticityquantum speed limitmixed-state fidelitymany-body systemsgapped phasesdriving ratethermodynamic limitLiouville space

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The pith

The finite-temperature threshold driving rate in gapped many-body systems factorizes into a zero-temperature size scaling and a universal temperature factor.

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

The paper derives bounds on the Hilbert-Schmidt fidelity for mixed states undergoing driven evolution using a mixed-state quantum speed limit and Liouville-space fidelity susceptibility. For local Hamiltonians in gapped phases these bounds give an explicit threshold driving rate separating adiabatic from nonadiabatic regimes. In the thermodynamic limit this threshold factorizes into a system-size term that matches zero-temperature adiabatic scaling and a temperature-dependent factor. The temperature factor stays exponentially close to one at low temperatures but becomes linear in temperature at high temperatures. This yields a largely model-independent criterion for finite-temperature adiabaticity in closed quantum many-body systems.

Core claim

By combining a mixed-state quantum speed limit with mixed-state fidelity susceptibility within the Liouville-space formulation of quantum mechanics, the authors derive rigorous bounds on the Hilbert-Schmidt fidelity between mixed states. For protocols that drive an initial Gibbs state toward a quasi-Gibbs target, these bounds yield an explicit threshold driving rate for the onset of nonadiabaticity. For a broad class of local Hamiltonians in gapped phases, in the thermodynamic limit, the threshold driving rate factorizes into a system-size contribution that recovers the zero-temperature scaling and a universal temperature-dependent factor. The latter is exponentially close to unity at low温度,

What carries the argument

The combination of a mixed-state quantum speed limit with mixed-state fidelity susceptibility in the Liouville-space formulation, which yields rigorous bounds on the Hilbert-Schmidt fidelity between mixed states to determine the threshold driving rate.

If this is right

The threshold provides an explicit and practical criterion for the onset of nonadiabaticity at finite temperature under closed-system unitary evolution.
In the thermodynamic limit the scaling cleanly separates into a system-size contribution and a temperature-dependent factor.
At low temperatures the finite-temperature correction remains exponentially small, recovering the zero-temperature adiabatic scaling.
At high temperatures the threshold driving rate grows linearly with temperature.
Verification in spin-1/2 chains produces closed-form expressions for the threshold that match the predicted scaling.

Where Pith is reading between the lines

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

The universal temperature factor supplies a simple multiplicative correction that can adjust zero-temperature adiabatic protocols for thermal effects without requiring full finite-temperature simulations.
The Liouville-space bounding technique could be extended to open-system dynamics by incorporating dissipative superoperators into the speed-limit and susceptibility expressions.
Experimental checks in quantum simulators could vary temperature and driving speed to test the linear high-T regime and identify any departures from the gapped-phase assumption.

Load-bearing premise

The factorization and bounds hold under the assumption that the driving protocol takes an initial Gibbs state to a quasi-Gibbs target state while the system remains in gapped phases throughout the thermodynamic limit.

What would settle it

Compute the onset of nonadiabaticity via fidelity or local observables in a driven spin-1/2 chain at varying temperatures and check whether the threshold rate follows the exact factorization with linear high-T scaling predicted by the closed-form expressions.

Figures

Figures reproduced from arXiv: 2602.01943 by Jyong-Hao Chen, Li-Ying Chou.

**Figure 2.** Figure 2: Temperature-dependent factor f(β) in the threshold driving rate Γth [Eqs. (10), (15)] for the TFIC and QXYC [Eq. (17)] in the thermodynamic limit. The solid curve shows the exact result f(β) = coth(2βJ) [Eq. (19)], while the dotted curves show the low- and high-temperature asymptotics, f(β) ≃ 1 + 2e −4βJ (low-temperature) and f(β) ≃ 1/(2βJ) (high-temperature). Vˆ differs between the two models: Vˆ TFIC =… view at source ↗

**Figure 3.** Figure 3: Adiabatic fidelity F(λ) [Eq. (9)] (cyan curve) and thermal-state overlap C(λ) [Eq. (12)] (black curve) for the driven transverse-field Ising chain Hˆ λ = Hˆ 0 + λVˆ TFIC (17a) at βJ = 5 and Γ/J = 2, plotted as a function of λ = h/J. Panels (a) and (b) correspond to N = 103 and N = 104 , respectively. Over the range shown, F(λ) and C(λ) are visually indistinguishable. The blue (resp., red) shaded region in… view at source ↗

read the original abstract

Establishing quantitative adiabaticity criteria at finite temperature remains substantially less developed than in the pure-state setting, even though realistic quantum systems are never at absolute zero. Here, by combining a mixed-state quantum speed limit with mixed-state fidelity susceptibility within the Liouville-space formulation of quantum mechanics, we derive rigorous bounds on the Hilbert-Schmidt fidelity between mixed states. Focusing on protocols that drive an initial Gibbs state toward a quasi-Gibbs target, these bounds yield an explicit threshold driving rate for the onset of nonadiabaticity. For a broad class of local Hamiltonians in gapped phases, we show that, in the thermodynamic limit, the threshold driving rate factorizes into a system-size contribution that recovers the zero-temperature scaling and a universal temperature-dependent factor. The latter is exponentially close to unity at low temperature, whereas at high temperature it is linear in temperature. We verify the predicted scaling in several spin-1/2 chains by obtaining closed-form expressions for the threshold driving rate. Our results provide a practical and largely model-independent criterion for finite-temperature adiabaticity in driven many-body systems under closed-system unitary evolution.

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

The paper derives a factorization of the finite-T adiabatic threshold into zero-T size scaling times a universal temperature factor, verified exactly on spin chains.

read the letter

The main thing to know is that the threshold driving rate for staying adiabatic at finite temperature factorizes into the usual zero-temperature system-size scaling multiplied by a temperature-dependent factor that sits near one at low T and grows linearly at high T, for gapped local Hamiltonians in the thermodynamic limit. They obtain this by combining mixed-state quantum speed limits with Liouville-space fidelity susceptibility to bound the Hilbert-Schmidt fidelity between an initial Gibbs state and a quasi-Gibbs target state under unitary driving. The bounds are presented as rigorous, and the factorization is checked with closed-form expressions on several spin-1/2 chains. What stands out is that the temperature factor emerges as largely model-independent once the gap condition holds, and the zero-T limit is recovered cleanly without extra fitting. The closed-form verifications on finite chains give a concrete handle on the scaling that goes beyond formal bounds. The softer spot is the thermodynamic-limit step. The derivation assumes the instantaneous spectrum remains gapped throughout the protocol and that the target state stays sufficiently close to quasi-Gibbs so that extensive corrections do not spoil the separation. The quantum speed limit and susceptibility tools do not automatically enforce these conditions at infinite size, and the explicit checks remain finite-size. If the full manuscript supplies additional estimates showing the gap stays open and the fidelity susceptibility stays extensive without contamination, the claim tightens; otherwise the clean factorization rests on those assumptions holding. This is useful for anyone working on adiabatic algorithms or many-body simulations who needs a quantitative rate criterion that accounts for realistic temperatures. A reader focused on quantum information or driven systems at nonzero temperature would find the scaling formula directly applicable. The work deserves a serious referee because the tools are standard, the result is explicit, and the finite-T extension is concrete enough to be checked in detail.

Referee Report

3 major / 2 minor

Summary. The manuscript derives rigorous bounds on the Hilbert-Schmidt fidelity between mixed states by combining mixed-state quantum speed limits with Liouville-space fidelity susceptibility. For driving protocols taking an initial Gibbs state to a quasi-Gibbs target, it obtains an explicit threshold driving rate for the onset of nonadiabaticity. In the thermodynamic limit for a broad class of local Hamiltonians in gapped phases, this threshold factorizes into a system-size contribution recovering the zero-temperature scaling and a universal temperature-dependent factor, which is exponentially close to unity at low temperature and linear in temperature at high temperature. The scaling is verified through closed-form expressions for several spin-1/2 chains.

Significance. If the central claims hold, the work provides a largely model-independent criterion for finite-temperature adiabaticity under unitary evolution, extending zero-temperature results to realistic thermal settings. The factorization into size-dependent and temperature-dependent parts, with explicit low- and high-temperature behaviors, offers practical guidance for driven many-body systems. The closed-form verifications on spin chains add concrete support to the general bounds.

major comments (3)

[thermodynamic limit discussion] The factorization of the threshold driving rate into a system-size contribution and a universal temperature-dependent factor in the thermodynamic limit assumes persistence of the gap throughout the protocol. The mixed-state QSL bounds do not explicitly control the Liouvillian spectrum to prevent gap closure in the L→∞ limit, which is necessary for the clean separation claimed.
[verification on spin chains] Closed-form expressions for the threshold rate are obtained only for finite-size spin-1/2 chains. The manuscript should provide estimates showing that the universal T-dependent factor survives the continuum extrapolation without deviation from the quasi-Gibbs target state or contamination by extensive contributions.
[main derivation of bounds] The central assumption that the driving protocol maintains a quasi-Gibbs target state relies on the mixed-state fidelity susceptibility remaining well-defined. Additional bounds on deviations under unitary evolution are needed, as the QSL alone does not automatically guarantee this in the thermodynamic limit.

minor comments (2)

Clarify the precise definition of the 'quasi-Gibbs target state' early in the manuscript, including how it differs from a true Gibbs state under the driving protocol.
Ensure consistent numbering and referencing of all equations in the bound derivations to improve readability.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading and insightful comments. We address each major comment below and outline the revisions we will make to strengthen the manuscript.

read point-by-point responses

Referee: The factorization of the threshold driving rate into a system-size contribution and a universal temperature-dependent factor in the thermodynamic limit assumes persistence of the gap throughout the protocol. The mixed-state QSL bounds do not explicitly control the Liouvillian spectrum to prevent gap closure in the L→∞ limit, which is necessary for the clean separation claimed.

Authors: We agree that the persistence of the gap is crucial for the factorization in the thermodynamic limit. Our derivation assumes a gapped phase throughout the protocol for the class of local Hamiltonians considered, as stated in the abstract and introduction. The mixed-state QSL bounds are applied in Liouville space where the spectrum is controlled by the assumption of a finite gap. To make this explicit, we will revise the thermodynamic limit discussion section to include a statement that the limit is taken with the gap Δ fixed and positive, ensuring no closure and thus the clean separation into size and T-dependent factors. This addresses the concern without altering the core results. revision: yes
Referee: Closed-form expressions for the threshold rate are obtained only for finite-size spin-1/2 chains. The manuscript should provide estimates showing that the universal T-dependent factor survives the continuum extrapolation without deviation from the quasi-Gibbs target state or contamination by extensive contributions.

Authors: The closed-form expressions are derived for finite-size chains to allow exact computation, but the scaling is shown to be consistent with the general bounds. We acknowledge the need for extrapolation discussion. We will add estimates in the verification section, based on the exact formulas, demonstrating that as system size increases, the T-dependent factor approaches the universal form without significant deviation or extensive contamination, as the fidelity remains close to the quasi-Gibbs state below the threshold. This will be included as a new paragraph with supporting analysis. revision: yes
Referee: The central assumption that the driving protocol maintains a quasi-Gibbs target state relies on the mixed-state fidelity susceptibility remaining well-defined. Additional bounds on deviations under unitary evolution are needed, as the QSL alone does not automatically guarantee this in the thermodynamic limit.

Authors: The quasi-Gibbs target is maintained by construction in the bounds, where the fidelity susceptibility defines the target, and the QSL provides an upper bound on the rate of change of the fidelity. In the thermodynamic limit, the bounds are extensive and prevent large deviations by the threshold rate scaling. We will add additional clarification and perhaps a lemma or remark bounding the deviations explicitly in the main derivation section to ensure the susceptibility remains well-defined and the target is preserved. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation combines established mixed-state QSL and fidelity susceptibility to obtain threshold factorization without self-referential reduction or fitted inputs.

full rationale

The paper starts from mixed-state quantum speed limits and Liouville-space fidelity susceptibility (established external results) to bound Hilbert-Schmidt fidelity for protocols driving Gibbs states to quasi-Gibbs targets. The thermodynamic-limit factorization of the threshold rate into an L-dependent zero-T piece and a universal T-dependent factor follows directly from these bounds under the stated gapped-phase assumption; closed-form verifications on finite spin-1/2 chains serve as independent checks rather than inputs. No equation reduces the claimed scaling to a self-definition, a fitted parameter renamed as prediction, or a load-bearing self-citation chain. The derivation remains self-contained against prior QSL literature.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The work rests on standard quantum-information tools without introducing new free parameters or postulated entities.

axioms (2)

domain assumption Mixed-state quantum speed limit applies to the unitary driving of Gibbs states
Invoked to bound the Hilbert-Schmidt fidelity between initial and target mixed states
domain assumption Fidelity susceptibility defined in Liouville space for mixed states
Combined with the speed limit to obtain explicit threshold rates

pith-pipeline@v0.9.0 · 5515 in / 1368 out tokens · 48730 ms · 2026-05-16T08:27:14.045760+00:00 · methodology

discussion (0)

Reference graph

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